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Chapter 14: Q. 22 (page 897)

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

f(x)=-4+3xat1

Short Answer

Expert verified

The derivative of given function at1 is 3.

Step by step solution

01

Step 1. Given Information  

We are given a function,

f(x)=-4+3x

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)=-4+3xf(1)=-4+3(1)=-4+3=-1

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�1-4+3x-(-1)x-1=limx鈫�13x-3x-1=limx鈫�13(x-1)x-1=limx鈫�13=3

Hence, the derivative of the function at 1is 3.

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