   Chapter 9.3, Problem 18E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
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. p ( q ) = 2 q 2 − 4 q + 5 ;   q  = 2

(a)

To determine

To calculate: The derivative of function f(q)=2q24q+5 at q=2 by the definition.

Explanation

Given Information:

The function f(q) is f(q)=2q24q+5.

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(q)=2q24q+5

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

f(q+h)=2(q+h)24(q+h)+5=2(q2+h2+2qh)

(b)

To determine

To calculate: The instantaneous rate of change of function f(q) at any value and at q=2 if f(q)=2q24q+5.

(c)

To determine

To calculate: The slope to the tangent of the graph y=f(q) at q=2 if f(q)=2q24q+5.

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