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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Given that the graph of f passes through the point (2, 5) and that the slope of its tangent line at (x, f(x)) is 3 − 4x, find f(1).

To determine

To find: The value of f(1) .

Explanation

Given Data:

The function f(x) passes through the point (2,5) and the slope of its tangent line at (x,f(x)) is (34x) .

Formula used:

The antiderivative function for the function xn is xn+1n+1+C .

Here, C is the constant.

The tangent of the function f(x) is f(x) .

As the tangent line of the function f(x) is given as (34x) , the function f(x) is (34x) .

f(x)=(34x)

Calculate the function f(x) from the tangent function f(x) as follows.

Calculation of f(x) :

Rewrite the function f(x)=(34x) as follows.

f(x)=4x1+3x0 (1)

From the antiderivative function formula, the antiderivative for the function in equation (1) is written as follows

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