   Chapter 9.3, Problem 17E ### 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. p ( q ) = 2 q 2 + q + 5 ;   q  = 10

(a)

To determine

To calculate: The derivative of function f(q)=2q2+q+5 at q=10 by using definition.

Explanation

Given Information:

The function f(q) is f(q)=2q2+q+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) is f(q)=2q2+q+5.

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

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

(b)

To determine

To calculate: The instantaneous rate of change of function f(q) at any value and q=10 if f(q)=2q2+q+5.

(c)

To determine

To calculate: The slope to the tangent of the graph y=f(q) at q=10 if f(q)=2q2+q+5.

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