.  (a) Sketch the graph of y = 2x2 over the interval [-1,1] (b) Let x be any point in the interval [-1,1] and let A(x) denote the area under the graph over the interval [-1,x]. It follows that A′(x) = 2x2. Find an expression including an arbitrary constant for A(x) (i.e. find a func- tion whose derivative is 2x2). Verify that the derivative of your expression gives A′(x) = 2x2. (c) Find the value of c in your expression by considering A(x), the area under the graph over [-1,x], when x = −1.

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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2. 
(a) Sketch the graph of y = 2x2 over the interval [-1,1]
(b) Let x be any point in the interval [-1,1] and let A(x) denote the area under the
graph over the interval [-1,x]. It follows that A′(x) = 2x2.
Find an expression including an arbitrary constant for A(x) (i.e. find a func-
tion whose derivative is 2x2). Verify that the derivative of your expression gives
A′(x) = 2x2.
(c) Find the value of c in your expression by considering A(x), the area under the
graph over [-1,x], when x = −1.

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