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Chapter 14: Q. 28 (page 897)

In Problems 21鈥�32, find the derivative of each function at the given number.

f(x)=2x3-x2at2

Short Answer

Expert verified

Derivative of the function at2is equal to20

Step by step solution

01

Step 1. Given information

Given function is f(x)=2x3-x2

We have to find the derivative of the given function at2

02

Step 2. Definition of derivative

Let's say a function y=f(x),

The derivative of the function at cis defined as

localid="1647080078052">f'(c)=limx鈫�cf(x)-f(c)x-c.

03

Step 3. Finding the derivative

By substituting the given function in the derivative definition,

we will get:

f'(2)=limx鈫�2f(x)-f(2)x-2鈬�f'(2)=limx鈫�2(2x3-x2)-(2路23-22)x-2鈬�f'(2)=limx鈫�2(2x3-x2)-12x-2

04

Step 4. Simplifying the limit

By rewriting the limit we will have:

f'(2)=limx鈫�22x3-x2-12x-2鈬�f'(2)=limx鈫�2(x-2)(2x2+3x+6)x-2鈬�f'(2)=limx鈫�2(2x2+3x+6)鈬�f'(2)=2(4)+3(2)+6鈬�f'(2)=20

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Most popular questions from this chapter

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