   Chapter 2.7, Problem 21E

Chapter
Section
Textbook Problem

If an equation of the tangent tine to the curve y = f(x) at the point where a = 2 is y = 4x – 5, find f(2) and f'(2).

To determine

To find: The value of the function f(x) and the derivative f(x) at the point a=2.

Explanation

Given:

The equation of the curve is y=f(x).

The equation of the tangent line to the curve is y=4x5 at a=2

Formula used:

The equation of the tangent line to the curve y=f(x) at the point (a,f(a)) is,

yf(a)=f(a)(xa) (1)

Calculation:

Obtain the value of the function f(x) and the derivative f(x) at the point a=2.

The graph of the tangent line touches the curve at (a,f(a)) is y=4x5. So that, the point (a,f(a)) is lies on the curve y=f(x) and also lies on the tangent line. That is, the value of the curve y=f(x) at a=2 is same as the value of the tangent line y=4x5 at a=2

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