2. In class, we matched functions to their derivatives. We will do that again, and match some properties too. Consider these four functions and their derivatives you matched earlier. f(r) f'() (i) 2 (A) -3 1 2 3 -3 -2 -1 -1 1 2 -2 -2 f(r) f(r) (ii) (B) 1 3 3 2 -1 2 1 2 -3 -2 1 -1 -2 2 f'r) f(x) (C) (ii) 2 -3 1 3 -2 2 1 -2 2 f(r) f(r) (D) (iv) 1 2 -3 -2 -1 -3 -2/ -1 1 2 1 -2 (a) Re-match the functions with their derivatives. (ii) B (1) C (6) D (iv) A (b) Determine which of the four properties corresponds to the functions above. Note that f"(x) is interpreted as the derivative of the derivative of f(x), etc. (p1) The derivative of f'(x) never switches sign. Corresponding function (number only): (p2) f(x) has a vertical tangent line at x -1. Corresponding function (number only): (p3) The derivative of f'(x) is undefined at x 1. Corresponding function (number only): 0. (p4) f'(x) and its derivative are zero at x 0 and only at 1 Corresponding function (number only): 3 A3 3. The graph of a function f(x) over -3, 31 is shown on the graph below. 3 -3 -2 -1 0 2 1 Sketch a plausible graph for f'() on the blank grid below. 0 -3 -2 -1 0 1 2 3

2. In class, we matched functions to their derivatives. We will do that again, and match some properties too. Consider these four functions and their derivatives you matched earlier. f(r) f'() (i) 2 (A) -3 1 2 3 -3 -2 -1 -1 1 2 -2 -2 f(r) f(r) (ii) (B) 1 3 3 2 -1 2 1 2 -3 -2 1 -1 -2 2 f'r) f(x) (C) (ii) 2 -3 1 3 -2 2 1 -2 2 f(r) f(r) (D) (iv) 1 2 -3 -2 -1 -3 -2/ -1 1 2 1 -2 (a) Re-match the functions with their derivatives. (ii) B (1) C (6) D (iv) A (b) Determine which of the four properties corresponds to the functions above. Note that f"(x) is interpreted as the derivative of the derivative of f(x), etc. (p1) The derivative of f'(x) never switches sign. Corresponding function (number only): (p2) f(x) has a vertical tangent line at x -1. Corresponding function (number only): (p3) The derivative of f'(x) is undefined at x 1. Corresponding function (number only): 0. (p4) f'(x) and its derivative are zero at x 0 and only at 1 Corresponding function (number only): 3 A3 3. The graph of a function f(x) over -3, 31 is shown on the graph below. 3 -3 -2 -1 0 2 1 Sketch a plausible graph for f'() on the blank grid below. 0 -3 -2 -1 0 1 2 3

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...

See similar textbooks

Similar questions

1) Calculate the problem in the image as an anti-derivative. Make sure to include all steps:
How can I find the derivative of Y With respect to X. Show me step by step please
Find a function with the given derivative whose graph passes through point P f'(x)=1/x+2, x is greater than -2, P(-1,3)
How may nonzero higher order derivatives are there?
Enter the value of g^{(10)}(0) -- the 10th derivative of g at x=0
Two equivalent forms of the Chain Rule for calculating the derivative of y = ƒ(g(x)) are presented in this section. State both forms.
1) Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the rate of variation. 2) Calculate the derivatives of the following functions
find the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)
10.Anti-derivative of y(2y^2-3)^5
What role does the denominator of f'(x) play in finding the critical points (in other words, what do we do with the denominator now that we have the derivative)?
show derivatives of : a. y = ex^3+5x3 b. y = ln(2x4+2)3
1. Determine the -values where relative extrema occur for y = (x ^ 2 + x - 12) ^ 2 . Use the second derivative test, if possible.