   Chapter 11, Problem 36RE Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 33-40, find all values of x (if any) where the tangent line to the graph of the given equation is horizontal. y = x 2 2 − 8 x 2

To determine

To calculate: The values of x (if any) where the tangent line to the graph of function y=x228x2 is horizontal.

Explanation

Given Information:

The provided function is y=x228x2.

Formula used:

Difference rule of the derivative is [fg](x)=f(x)g(x).

Constant multiple rule of the derivative is f(cx)=cf(x), where c is any constant.

The slope of the tangent of the graph f(x) at the point (a,b) is given by f(a).

Power rule of a function y=xn is dydx=nxn1, where n is some constant.

Calculation:

Consider the function, y=x228x2

Find the slope of the tangent of the graph of the function y=x228x2 by determining the derivative of the function f(x).

Convert the function in power form,

y=x228x2

Apply difference rule of derivative to the function y=x228x2 with respect to x,

ddx(y)=ddx(x228x2

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