   Chapter 11.1, Problem 70E 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 65–70, find all values of x (if any) where the tangent line to the graph of the given equation is horizontal. [HINT: The tangent line is horizontal when its slope is zero.] y = x − x

To determine

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

Explanation

Given Information:

The function is y=xx.

Formula used:

Difference rule of derivative is [fg](x)=f(x)g(x), where f(x) and g(x) are any two functions.

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

Calculation:

Consider the function, y=xx

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

Rewrite the function,

y=xx12

Apply difference rule of derivative to the function y=xx12 with respect to x,

dydx=ddx(x)ddx(x12)

Apply power rule,

dy

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