Solutions for Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)
Problem 2CYU:
Let f(x)=1/x4. a. Find its derivative. b. Find f(2).Problem 1E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 2E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 3E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 4E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 5E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 6E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 7E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 8E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 9E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 10E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 11E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 12E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 13E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 14E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 15E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 16E:
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions....Problem 17E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x3 at x=12.Problem 18E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x5 at x=32.Problem 19E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=1x at x=23.Problem 20E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=13 at x=2.Problem 21E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x+11 at x=0.Problem 22E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x1/3 at x=8.Problem 23E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=x at x=116.Problem 24E:
In Exercises 1724, find the derivative of f(x) at the designated value of x. f(x)=1x25 at x=32.Problem 25E:
Find the slope of the curve y=x4 at x=2.Problem 26E:
Find the slope of the curve y=x5 at x=13.Problem 27E:
If f(x)=x3, compute f(5) and f(5).Problem 28E:
If f(x)=2x+6, compute f(0) and f(0).Problem 29E:
If f(x)=x1/3, compute f(8) and f(8).Problem 30E:
If f(x)=1/x2, compute f(1) and f(1).Problem 31E:
If f(x)=1/x5, compute f(2) and f(2).Problem 32E:
If f(x)=x3/2, compute f(16) and f(16).Problem 33E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 34E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 35E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 36E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 37E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 38E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 39E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 40E:
In Exercises 33-40, find an equation of the tangent line to the graph y=f(x) at the given x. Do not...Problem 41E:
The point-slope form of the equation of the tangent line to the graph of y=x4 at point (1,1) is...Problem 42E:
The tangent line to the graph of y=1x at the point P=(a,1a), where a0, is perpendicular to the line...Problem 43E:
The line y=2x+b is tangent to the graph y=x at the point P=(a,a). Find P and determine b.Problem 45E:
a. Find the point on the curve y=x where the tangent line is parallel to the line y=x8. b. On the...Problem 46E:
There are two points on the graph of y=x3 where the tangent lines are parallel to y=x. Find these...Problem 47E:
Is there any point on the graph of y=x3 where the tangent line is perpendicular to y=x? Justify your...Problem 48E:
The graph of y=f(x) goes through the point (2, 3) and the equation of the tangent line at that point...Problem 59E:
In Fig.15, the straight line y=14x+b is tangent to the graph of f(x)=x. Find the values of a and b....Problem 60E:
In Fig.16, the straight line is tangent to the graph of f(x)=1x. Find the value of a. Figure 16Problem 65E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 66E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 67E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 68E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 69E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 70E:
In Exercises 65-70, compute the difference quotient f(x+h)f(x)h. Simplify your answer as much as...Problem 71E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 72E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 73E:
In Exercises 71-76, apply the threestep method to compute the derivative of the given function....Problem 74E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 75E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 76E:
In Exercises 71-76, apply the three step method to compute the derivative of the given function....Problem 77E:
Draw two graphs of your choice that represent a function y=f(x) and its vertical shift y=f(x)+3 Pick...Problem 78E:
Use the approach of Exercise 77 to show that ddxf(x)=ddx(f(x)+c) For any costant c.[Hint: Compare...Problem 81E:
Technology Exercises In Exercises 79-84, use a derivative routine to obtain the value of the...Problem 82E:
Technology Exercises In Exercises 79-84, use a derivative routine to obtain the value of the...Browse All Chapters of This Textbook
Chapter 0 - FunctionsChapter 0.1 - Functions And Their GraphsChapter 0.2 - Some Important FunctionsChapter 0.3 - The Algebra Of FunctionsChapter 0.4 - Zeros Of Functions—the Quadratic Formula And FactoringChapter 0.5 - Exponents And Power FunctionsChapter 0.6 - Functions And Graphs In ApplicationsChapter 1 - The DerivativeChapter 1.1 - The Slope Of A Straight LineChapter 1.2 - The Slope Of A Curve At A Point
Chapter 1.3 - The Derivative And LimitsChapter 1.4 - Limits And The DerivativeChapter 1.5 - Differentiability And ContinuityChapter 1.6 - Some Rules For DifferentiationChapter 1.7 - More About DerivativesChapter 1.8 - The Derivative As A Rate Of ChangeChapter 2 - Applications Of The DerivativeChapter 2.1 - Describing Graphs Of FunctionsChapter 2.2 - The First- And Second-derivative RulesChapter 2.3 - The First- And Second-derivative Tests And Curve SketchingChapter 2.4 - Curve Sketching (conclusion)Chapter 2.5 - Optimization ProblemsChapter 2.6 - Further Optimization ProblemsChapter 2.7 - Applications Of Derivatives To Business And EconomicsChapter 3 - Techniques Of DifferentiationChapter 3.1 - The Product And Quotient RulesChapter 3.2 - The Chain RuleChapter 3.3 - Implicit Differentiation And Related RatesChapter 4 - The Exponential And Natural Logarithm FunctionsChapter 4.1 - Exponential FunctionsChapter 4.2 - The Exponential Function ExChapter 4.3 - Differentiation Of Exponential FunctionsChapter 4.4 - The Natural Logarithm FunctionChapter 4.5 - The Derivative Of Ln XChapter 4.6 - Properties Of The Natural Logarithm FunctionChapter 5 - Applications Of The Exponential And Natural Logarithm FunctionsChapter 5.1 - Exponential Growth And DecayChapter 5.2 - Compound InterestChapter 5.3 - Applications Of The Natural Logarithm Function To EconomicsChapter 5.4 - Further Exponential ModelsChapter 6 - The Definite IntegralChapter 6.1 - AntidifferentiationChapter 6.2 - The Definite Integral And Net Change Of A FunctionChapter 6.3 - The Definite Integral And Area Under A GraphChapter 6.4 - Areas In The Xy-planeChapter 6.5 - Applications Of The Definite IntegralChapter 7 - Functions Of Several VariablesChapter 7.1 - Examples Of Functions Of Several VariablesChapter 7.2 - Partial DerivativesChapter 7.3 - Maxima And Minima Of Functions Of Several VariablesChapter 7.4 - Lagrange Multipliers And Constrained OptimizationChapter 7.5 - The Method Of Least SquaresChapter 7.6 - Double IntegralsChapter 8 - The Trigonometric FunctionsChapter 8.1 - Radian Measure Of AnglesChapter 8.2 - The Sine And The CosineChapter 8.3 - Differentiation And Integration Of Sin T And Cos TChapter 8.4 - The Tangent And Other Trigonometric FunctionsChapter 9 - Techniques Of IntegrationChapter 9.1 - Integration By SubstitutionChapter 9.2 - Integration By PartsChapter 9.3 - Evaluation Of Definite IntegralsChapter 9.4 - Approximation Of Definite IntegralsChapter 9.5 - Some Applications Of The IntegralChapter 9.6 - Improper IntegralsChapter 10 - Differential EquationsChapter 10.1 - Solutions Of Differential EquationsChapter 10.2 - Separation Of VariablesChapter 10.3 - First-order Linear Differential EquationsChapter 10.4 - Applications Of First-order Linear Differential EquationsChapter 10.5 - Graphing Solutions Of Differential EquationsChapter 10.6 - Applications Of Differential EquationsChapter 10.7 - Numerical Solution Of Differential EquationsChapter 11 - Taylor Polynomials And Infinite SeriesChapter 11.1 - Taylor PolynomialsChapter 11.2 - The Newton–raphson AlgorithmChapter 11.3 - Infinite SeriesChapter 11.4 - Series With Positive TermsChapter 11.5 - Taylor SeriesChapter 12 - Probability And CalculusChapter 12.1 - Discrete Random VariablesChapter 12.2 - Continuous Random VariablesChapter 12.3 - Expected Value And VarianceChapter 12.4 - Exponential And Normal Random VariablesChapter 12.5 - Poisson And Geometric Random Variables
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