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For example, an antiderivative for y = 2x is x² + 5 because (x² + 5) = 2x = y. However, the antiderivative of f(x) for any given function is NOT unique. Because if we add any constant to the antiderivative of f(x), we can still get f(x) when we differentiate it. (a) Give one antiderivative of f(x) = 17: (b) Differentiate your answer in (a) to show that the antiderivative of your answer is indeed 2 ²+8r+17'

For example, an antiderivative for y = 2x is x² + 5 because (x² + 5) = 2x = y. However, the antiderivative of f(x) for any given function is NOT unique. Because if we add any constant to the antiderivative of f(x), we can still get f(x) when we differentiate it. (a) Give one antiderivative of f(x) = 17: (b) Differentiate your answer in (a) to show that the antiderivative of your answer is indeed 2 ²+8r+17'

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Let f(x) be a function. We say that F(x) is an antiderivative of f(x) if
F0(x) = f(x) for all x in the domain of f(x).

Let f(x) be a function. We say that F(x) is an antiderivative of f(x) if F'(x) = f(x) for all x in the domain of f(x). For example, an antiderivative for y = 2x is x² + 5 because (x² + 5) = 2x = y. However, the antiderivative of f(x) for any given function is NOT unique. Because if we add any constant to the antiderivative of f(x), we can still get f(x) when we differentiate it. (a) Give one antiderivative of f(x) = 17: 1²+8x+17' (b) Differentiate your answer in (a) to show that the antiderivative of your answer is 2 1²+8x+17*
Transcribed Image Text:Let f(x) be a function. We say that F(x) is an antiderivative of f(x) if F'(x) = f(x) for all x in the domain of f(x). For example, an antiderivative for y = 2x is x² + 5 because (x² + 5) = 2x = y. However, the antiderivative of f(x) for any given function is NOT unique. Because if we add any constant to the antiderivative of f(x), we can still get f(x) when we differentiate it. (a) Give one antiderivative of f(x) = 17: 1²+8x+17' (b) Differentiate your answer in (a) to show that the antiderivative of your answer is 2 1²+8x+17*
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