   Chapter 2.8, Problem 24E

Chapter
Section
Textbook Problem

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative.f(x) = 4 + 8x – 5x2

To determine

To find: The derivative of the function f(x)=4+8x5x2 and state the domain of the function and its derivative.

Explanation

Formula used:

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

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

Calculation:

Obtain the derivative of the function f(x).

Compute f(x) by using the equation (1),

f(x)=limh0f(x+h)f(x)h=limh0(4+8(x+h)5(x+h)2)(4+8x5x2)h=limh0(4+8x+8h5(x2+h2+2xh))(4+8x5x2)h=limh04+8x+8h5x25h210xh

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