   Chapter 9.3, Problem 16E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# For each function in Problems 15-18, find(a) the derivative using the definition.(b) the instantaneous rate of change of the function any value and at the given value.(c) the slope of the tangent at the given value. f ( x ) = 16 x 2 − 4 x + 2 ;    x  = 1

(a)

To determine

To calculate: The derivative of function f(x)=16x24x+2 at x=1 by using definition.

Explanation

Given Information:

The function f(x) is f(x)=16x24x+2.

Formula used:

If a function f(x) is defined in the interval [x+h,x], then its derivative is given by the formula,

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

Calculation:

Consider the function f(x) is f(x)=16x24x+2.

Substitute x=x+h in f(x) to get,

f(x+h)=16(x+h)24(x+h)+2=16(x2+h2+2xh

(b)

To determine

To calculate: The instantaneous rate of change of function f(x) at x=1 if f(x)=16x24x+2.

(c)

To determine

To calculate: The slope to the tangent of the graph y=f(x) at x=2 if f(x)=16x24x+2.

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