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Chapter 10: Q. 43 (page 777)

Use the definition of the derivative to find f'for each function fin Exercises 39-54

f(x)=2x+1

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information

The given functionf(x)=2x+1f(x)=2x+1

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)=2x+1then

f(x+h)=2(x+h)+1

Putting these values in (1)

f'(x)=limh鈫�02(x+h)+1-2x+1h=limh鈫�02(x+1)-2(x+h+1)(x+h+1)(x+1)h=limh鈫�02x+2-2x-2h-2(x+h+1)(x+1)h=limh鈫�0-2h(x+h+1)(x+1)h=limh鈫�0-2h(x+h+1)(x+1)脳1h=limh鈫�0-2(x+h+1)(x+1)

Putting h=0

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

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

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