Answer True or False to each of the following statements.a) The function f(x)4is continuous at x= 2.x - 2b) The instantaneous rate of change of a function at a point is represented graphically as the slope of theline tangent to the curve at that point.c) The derivative of a linear function is constant.d) If y = f(x) , then the units of f'(x) are the units of x over the units of y.e) The function f(x)x + 3 is differentiable at x=-3.f) If a function is differentiable at a point, then the function is also necessarily continuous at that point.

We have to find As per our guidelines we have to solve three subparts

Answered: Answer True or False to each of the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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How would a small change in your average gas mileage (in miles/gallon) change the number of gallons of gas you use per month? More specifically, do the following: (a) Give numerical evidence that supports or refutes the claim that a small change in your average gas mileage results in an approrimately small change in the number of gallons of gas you use each month. Choose the distance you drive each month (and keep this constant) and then at least two significantly different values for the average gas mileage. Approrimate the proportionality constant in each case (if it erists) and write the proportionality approxima- tions. Be sure to define the appropriate variables and pay particular attention to units. (b) Using your results from part (a), approximate the proportionality con- stants that relate the small relative change in the number of gallons of gas
4. Explain the steps to find the derivative of the given function using the first principles y = √√x = 5 -
Solve for the derivative of the following function, give detailed computation
1. Determine the derivative of: f (x) = 4x3 – x² + 5x + 9
The graph below is the derivative of the function y = f(x) on the interval x [-3,10. Suppose f(x) is continuous and f(-1) = 1. Determine the value of the original function f(x) at x = -3, x = -2, and x = 1. Enter f(-2) in the blank below.
Find the derivative by the definition of each of the following functions: - 1- y = 2x2-3x 2- yv1+2x
In the first derivative of a function is a constant then the function is LINEAR. (A) True B) False
Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. Consider the graph of the function y = f(x) given in the figure. The x y-coordinate plane is given. There is a curve with seven points on the curve (2 unlabeled and 5 labeled) and four labeled intervals on the graph. The curve enters the window in the second quadrant, goes up and right, passes through the first unlabeled point, passes through the second unlabeled point, changes direction at point A on the positive y-axis, goes down and right, passes through the point B, changes direction at point C, goes up and right, passes through point D, changes direction at point E, goes down and right and exits the window in the first quadrant. Interval a begins at the first unlabeled point and ends at the second unlabeled point. Interval b begins at the first unlabeled…
i.) Piecewise functions: a. have limits for their entire domain b. have a domain of xER c. none of the other answers are correct d. never have limits for their entire domain ii.) The instantaneous rate of change for the function of f(x) equals the derivative of f(x): a. True b. False
9) Find the second derivative of the function given below and evaluate it for x=1

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