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Chapter 14: Q. 24 (page 897)

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

f(x)=2x2+1at-1

Short Answer

Expert verified

The derivative of given function at -1is -4.

Step by step solution

01

Step 1. Given Information  

We are given a function,

f(x)=2x2+1

We have to find the derivative of the given function at -1.

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=-1

f(x)=2x2+1f(-1)=2(-1)2+1=2+1=3

03

Step 3. Finding the derivative 

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

f'(-1)=limx鈫�-1f(x)-f(-1)x-(-1)=limx鈫�-12x2+1-3x+1=limx,12x2-2x+1=limx鈫�-12x2-1x+1=limx鈫�-12(x+1)(x-1)x+1=limx鈫�-12(x-1)=2(-1-1)=-4

Hence, the derivative of the function at-1 is -4.

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