Let f(x) and g(x) be functions whose graphs are shown below. Which of thefollowing statements is/are true?I. If h(x) = f(x)+ g(x), then h'(2) is negative.II. If h(x) = f(x)g(x), then h'(2) = 0.f(x)III. If h(x) =g(x)'then h'(2) is positive.6xyf(x)شا54321A. I onlyB. III onlyC. II and III only9(x)1 234567MacBook Pro2x8

We are asked about the derivative of the function h given a graph of the functions f and g. Note…

Answered: Let f(x) and g(x) be functions whose…

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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Suppose that f(x) and g(x) are each one-to-one functions. Suppose also that f(2) = 5, f(5) = 6, g(6) = 5, g(5)= 3.5, and that g(2) = 6. Compute 1. f-¹ (g(6)) 2. f(g-¹ (6)) 3. g=¹(f(2)) = | 4. g(f ¹(5)) = =
2. Consider the function f (x) = x¹ − 2x² + 3. (a) Find the intervals on which f is increasing / decreasing. (b) Find the intervals on which f is concave up/ concave down. Display your answer in table form, with a column for the intervals, columns for each factor, a column for the derivative, and a column for the function, as shown in lecture.
Letf, g be functions. Suppose we know that ƒ(−6) = 4, ƒ'(−6) = −4, g(−6) = −4, g′(−6) = −3. Using the above information, compute h' (-6) where h(x) = (f(x))² g(x). h'(- 6) = Number
The graph of f(x) is shown on the interval -5sxs5. -5 Determine whether each is less than, greater than or equal to 0. Assume f is twice differentiable. f(x) f'(x) f"(x)
Suppose that f(x) and g(x) are two functions and we know that: f(-3) = 2 g(-3) = 5 f'(-3) g'(-3) Find the following: (ƒ − g)'(−3) = (g - f)'(-3) = -1 -2 == (fg)'(-3) = (4) - '(-3) = f(x) x² If k(x) = = = then k'(-3)
Given f(-6) = 17,ƒ'(-6) = -2, g(-6)= -3, and g'(-6)= 2, find the value of h'(-6) based on the function below. h(x) = f(x) g(x) h'(- 6) = Keypad Keyboard Shortcuts
Consider the following function. f(x) = x4 – 8x3 + 18x² + 4 | (a) Make a sign diagram for the first derivative. ---Select--- v ---Select--- v ---Select--- v ---Select--- v ---Select--- v X = X = (b) Make a sign diagram for the second derivative. ---Select--- v ---Select--- v ---Select--- v ---Select--- v ---Select--- v X = X = (c) Sketch the graph, showing all relative extreme points and inflection points. y 40 y 40 Delete PriSc GOO0 F11 Invsert DP F10 F12 DIB F7 F9 F8 Backspace Num Lock F6 F5 F4 F3 Esc F2 FnLock %23 %24 7 8. 4 Hos 1 Y W E Enter J K + // CO %#3

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