1 Functions And Limits 2 Derivatives 3 Applications Of Differentiation 4 Integrals 5 Applications Of Integration 6 Inverse Functions 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Infinite Sequences And Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus 17 Second-order Differential Equations expand_more
2.1 Derivatives And Rates Of Change 2.2 The Derivative As A Function 2.3 Differentiation Formulas 2.4 Derivatives Of Trigonometric Functions 2.5 The Chain Rule 2.6 Implicit Differentiation 2.7 Rates Of Change In The Natural And Social Sciences 2.8 Related Rates 2.9 Linear Approximations And Differentials 2.R Review 2.P Problem Plus expand_more
Problem 1E: Use the given graph to estimate the value of each derivative. Then sketch the graph of f. a f(3) b... Problem 2E: Use the given graph to estimate the value of each derivative. Then sketch the graph of f. a f(0) b... Problem 3E: Match the graph of each function in ab with the graph of its derivative in IIV. Give reasons for... Problem 4E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 5E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 6E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 7E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 8E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 9E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 10E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 11E: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Then use... Problem 12E: Shown is the graph of the population function P(t) for yeast cells in a laboratory culture. Use the... Problem 13E: A rechargeable battery is plugged into a charger. The graph shows C(t) the percentage of full... Problem 14E: The graph from the US Department of Energy shows how driving speed affects gas mileage. Fuel economy... Problem 15E: The graph shows how the average age M of first marriage of Japanese men varied in the last half of... Problem 16E: Make a careful sketch of the graph of the sine function and below it sketch the graph of its... Problem 17E: Let f(x)=x2. a Estimate the values of f(0),f(12),f(1), and f(2) by using a graphing device to zoom... Problem 18E: Let f(x)=x3. a Estimate the values of f(0),f(12),f(1),f(2), and f(3) by using a graphing device to... Problem 19E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 20E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 21E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 22E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 23E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 24E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 25E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 26E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 27E: Find the derivative of the function using the definition of derivative. State the domain of the... Problem 28E Problem 29E Problem 30E: a Sketch the graph of f(x)=6x by starting with the graph of y=x and using the transformations of... Problem 31E Problem 32E Problem 33E Problem 34E: The table gives the number N(t), measured in thousands, of minimally invasive cosmetic surgery... Problem 35E Problem 36E Problem 37E: Let P represent the percentage of a citys electrical power that is produced by solar panels t years... Problem 38E Problem 39E: The graph of f is given. State, with reasons, the numbers at which f is not differentiable. Problem 40E: The graph of f is given. State, with reasons, the numbers at which f is not differentiable. 40. Problem 41E: The graph of f is given. State, with reasons, the numbers at which f is not differentiable. Problem 42E: The graph of f is given. State, with reasons, the numbers at which f is not differentiable. 42. Problem 43E Problem 44E Problem 45E: The graphs of a function f and its derivative f are shown. Which is bigger, f(1)orf(1)? Problem 46E: The graphs of a function f and its derivative f are shown. Which is bigger, f(1)orf(1)? Problem 47E: The figure shows the graphs of f,f,andf. Identify each curve, and explain your choices. Problem 48E: The figure shows graphs of f,f,f,andf. Identify each curve, and explain your choices. Problem 49E: The figure shows the graphs of three functions. One is the position function of a car, one is the... Problem 50E: The figure shows the graphs of four functions. One is the position function of a car, one is the... Problem 51E: Use the definition of a derivative to find f(x) and f(x). Then graph f,f,andf on a common screen and... Problem 52E Problem 53E Problem 54E: a The graph of a position function of a car is shown, where .s is measured in feet and t in seconds.... Problem 55E Problem 56E Problem 57E: Show that the function f(x)=|x6| is not differentiable at 6. Find a formula for f and sketch its... Problem 58E: Where is the greatest integer function f(x)=x not differentiable? Find a formula for f and sketch... Problem 59E Problem 60E: a Sketch the graph of the function g(x)=x+|x|. b For what values of x is g differentiable? c Find a... Problem 61E Problem 62E: The left-hand and right-hand derivatives of f at a are defined by f(a)=limh0f(a+h)f(a)h and... Problem 63E: Nick starts jogging and runs faster and faster for 3 mintues, then he walks for 5 minutes. He stops... Problem 64E Problem 65E: Let l be the tangent line to the parabola y=x2 at the point (1,1). The angle of inclination of l. is... format_list_bulleted