   Chapter 2, Problem 39RE

Chapter
Section
Textbook Problem

(a) Use the definition of a derivative to find f'(2). where f(x) = x3 – 2x.(b) Find an equation of the tangent Line to the curve y = x3 – 2x at the point (2, 4).(c) Illustrate pan (b) by graphing the curve and the tangent line on the same screen.

(a)

To determine

To find: The derivative of the function f(x)=x32x at x=2.

Explanation

Formula used:

The derivative of a function f at a number a, denoted by f(a) is,

f(a)=limh0f(a+h)f(a)h (1)

Calculation:

Obtain the derivative of the function f(x) at x=2.

Compute f(2) by using the equation (1).

f(2)=limh0f(2+h)f(2)h=limh0((2+h)32(2+h))((2)32(2))h=limh0(2+h)32(2+h)(84)h=limh0

(b)

To determine

To find: The equation of the tangent line to the curve at the point (2, 4).

(c)

To determine

To sketch: The graph of the curve and the tangent line.

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