   Chapter 11.1, Problem 106E 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 3 and g ( x ) = x 3 + 3 . How do the slopes of the tangent lines of f and g compare?

To determine

The comparison of the slope of tangent to the functions f(x)=x3 and g(x)=x3+3.

Explanation

Given Information:

The provided functions are f(x)=x3 and g(x)=x3+3.

Consider the provided functions f(x)=x3 and g(x)=x3+3,

To calculate the slope of the tangent to the function f(x)=x3 differentiate the function on each side with respect to x.

ddx[f(x)]=ddx(x3)

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)=x3,

f(x)=3x31=3x2

Thus, the derivative of function f(x)=x3 is f(x)=3x2.

Similarly, to calculate the slope of the tangent to the function g(x)=x3+3 differentiate the function on each side with respect to x.

The constant multiple rule of derivative of function f(x) is f(cx)=cf(x) where, c is constant

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