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Chapter 14: Q. 23 (page 897)

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

f(x)=x2-3at0

Short Answer

Expert verified

The derivative of given function at 0is 0.

Step by step solution

01

Step 1. Given Information  

We are given a function,

f(x)=x2-3

We have to find the derivative of the given function at 0.

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=0

f(x)=x2-3f(0)=(0)2-3=-3

03

Step 3. Finding the derivative 

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

f'(0)=limx鈫�0f(x)-f(0)x-0=limx鈫�0x2-3-(-3)x=limx鈫�0x2x=limx鈫�0x=0

Hence, the derivative of the function at0 is 0.

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