Answered: a. Find the derivative ƒ'(x) 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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Question

a. Find the derivative ƒ'(x) of the given function y = ƒ(x).
b. Graph y = ƒ(x) and y = ƒ'(x) side by side using separate
sets of coordinate axes, and answer the following questions.
c. For what values of x, if any, is ƒ' positive? Zero? Negative?
d. Over what intervals of x-values, if any, does the function
y = ƒ(x) increase as x increases? Decrease as x increases?
How is this related to what you found in part (c)? y = x4/4

Expert Solution

Step 1

$G i v e n : y = f (x) = \frac{x^{4}}{4} a) w e h a v e t o f i n d t h e d e r i v a t i v e f' (x) o f t h e g i v e n f u n c t i o n y = f (x) f' (x) = \frac{d}{d x} f (x) = \frac{4 x^{4 - 1}}{4} = \frac{4 x^{3}}{4} = x^{3}$

b) firstly the graph of y=f(x) is drawn below:

then graph of f'(x) is drawn below:

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