   Chapter 11.1, Problem 105E 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

Consider f ( x ) = x 2 and g ( x ) = 2 x 2 =. How do the slopes of the tangent lines of f and g the same x compare?

To determine

The comparison of the slope of tangent to the functions f(x)=x2 and g(x)=2x2.

Explanation

Given Information:

The provided functions are f(x)=x2 and g(x)=2x2.

Consider the provided functions f(x)=x2 and g(x)=2x2,

To calculate the slope of the tangent to the function f(x)=x2 differentiate the function on each side with respect to x.

ddx[f(x)]=ddx(x2)

The derivative of the function f(x)=xn by using power rule, is f(x)=nxn1.

Apply power rule to differentiate the function f(x)=x2,

f(x)=2x21=2x

Thus, the derivative of function f(x)=x2 is f(x)=2x

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