How can a linear approximation be used to approximate the value of a functionf near a point at which f and f' are easily evaluated? Choose the correct answer below. O A. Iffis differentiable at the point, then near that point, f is approximately linear; so, the function nearly coincides with the tangent line at that point. O B. Iffis differentiable at the point, then near that point, f is nonlinear; so, the function is equal to the tangent line at that point. OC. Iffis differentiable at the point, then near that point, f is approximately linear; so, the function is equal to the tangent line at that point. O D. Iff is differentiable at the point, then near that point, f is approximately linear; so every function value is less than the value of the tangent line at that point.

Q: 7:³ 5x² Consider the function f(x) = - + 3 +2x10. 3 The tangent line through the point (3, 2) is…

A:

Q: 5y4+7=x4-3y; x=3, y=-2

A: To find slope of a line tangent to the given curve at a given point. To make a sketch of this…

Q: Evaluate the indefinite integral. 15 + x*dx + C

A: Using Integration by substitution.

Q: a. Use the Quotient Rule to find the derivative of the given function.Simplify your result.b. Find…

A: The given function is fw=w3-ww

Q: a. Graph the function f(x)=x²-8x+12. b. Identify the point (a,f(a)) at which the function has a…

A: The given function .We have to find an accurate conjecture for the slope of the tangent line at .

Q: a 1. The graph of y = where a is a constant is called the witch of Agnessi (named after 2 x²+a² the…

A: To find the derivative and equation of line tangent to the given curve.

Q: Select ALL possible answers if there is more than one. Below shows the graphs of the slopes of the…

A: The slope of the tangent line represent the derivative of the function.

Q: Question 2. A function f(x) satisfies f(x+h)-f(x)=x+h+z² · h² + 4h³ for all z and h. Use Fermat's…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find an equation of the tangent line to the graph of f at the given point. Be sure to include all…

A: Differentiate at given point and then use equation of  tangent  line

Q: The following function gives the average cost (in dollars) per advertisement when paying for X…

A: Multiple sub-parts question-"As per our guidelines we are suppose to answer only first 3…

Q: 20. Zenzizenzicube is an obsolete word that represents the square of the square of a cube, In…

A: Given:x322

Q: 2. The expression f(2)= 8 = x(3) gives the slope at any point on the graph of the function f(x)…

A: Given The curve:Aim:A. To find the equation of the tangent to  at point B. To find an expression for…

Q: Using the definition of a derivative, what is y'(z) given that y(z) = z* +z² – 5z +3? (Do not…

A: Here we are going to solve only one question and for the remaining question post the question again.…

Q: f(x) = x³ - 2x - 6

A: Given that the function fx=x3-2x-6The point -1,-5

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: