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Chapter 14: Q. 26 (page 897)

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

f(x)=3x2-4xat2

Short Answer

Expert verified

The derivative of given function at 2is 8.

Step by step solution

01

Step 1. Given Information  

We are given a function,

f(x)=3x2-4x

We have to find the derivative of the given function at 2.

02

Step 2. Definition of derivative  

The derivative of the function at c is defined as,

f'(c)=limx鈫�cf(x)-f(c)x-c

Here, c=2

f(x)=3x2-4xf(2)=3(2)2-4(2)=12-8=4

03

Step 3. Finding the derivative 

By substituting the given function in the derivative definition, we get

f'(2)=limx鈫�2f(x)-f(2)x-2=limx鈫�23x2-4x-4x-2=limx鈫�2(3x+2)(x-2)x-2=limx鈫�2(3x+2)=3(2)+2=6+2=8

Hence, the derivative of the function at2 is 8.

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