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Chapter 2: Q. 44 (page 184)

Use the definition of the derivative to find f'for each function fin Exercises39-54

f(x)=21-x

Short Answer

Expert verified

The value off'(x)=2(1-x)2

Step by step solution

01

Step 1. Given information

The given functionf(x)=21-x

02

Step 2. Finding the value of f'(x)

We know that f'(x)=limh鈫�0f(x+h)-f(x)h.........(1)

Given f(x)=21-xthen

f(x+h)=21-(x+h)=21-x-h

Putting these values in(1)

f'(x)=limh鈫�021-x-h-21-xh=limh鈫�02(1-x)-2(1-x-h)(1-x-h)(1-x)h=limh鈫�02-2x-2+2x+2h(1-x-h)(1-x)h=limh鈫�02h(1-x-h)(1-x)h=limh鈫�02h(1-x-h)(1-x)脳1h=limh鈫�02(1-x-h)(1-x)

Put h=0

=2(1-x-0)(1-x)=2(1-x)(1-x)=2(1-x)2

Hence,the value off'(x)=2(1-x)2

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