   Chapter 9.3, Problem 15E ### 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 ) = 5 x 2 + 6 x − 11 ;    x  = 1

(a)

To determine

To calculate: The derivative of function f(x)=5x2+6x11 at x=2 by using definition.

Explanation

Given Information:

The function f(x) is f(x)=5x2+6x11.

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)=5x2+6x11.

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

f(x+h)=5(x+h)2+6(x+h)11=5(x2+h2+2x

(b)

To determine

To calculate: The instantaneous rate of change of function f(x) at any value and at x=2 if f(x)=5x2+6x11.

(c)

To determine

To calculate: The slope to the tangent of the graph y=f(x) at x=2 if f(x)=5x2+6x11.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 4143, find the distance between the two points. 43. (12,3) and (12,23)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Convert the expressions in Exercises 6584 to power form. 3x25472x3

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Given: 13 Prove: mn

Elementary Geometry For College Students, 7e

#### The gradient vector field for is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Find an expression for the mean of the probability density function .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Describe the elements of an abstract.

Research Methods for the Behavioral Sciences (MindTap Course List) 