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Chapter 10: Q. 5 (page 777)

Use the definition of the derivative to calculate the derivative of f(x)=x at c=4. At some point you will need to multiply numerator and denominator by the conjugate of 4+h-2, which is 4+h+2.

Short Answer

Expert verified

The derivative is 14.

Step by step solution

01

Step 1. Given Information. 

We are given a function,

f(x)=x

02

Step 2. Finding the derivative. 

The derivative is given by,

f'(c)=limh鈫�0f(c+h)-f(c)hf'(4)=limh鈫�04+h-4h=limh鈫�04+h-2h脳4+h+24+h+2=limh鈫�04+h-4h(4+h+2)=limh鈫�0hh(4+h+2)=limh鈫�014+h+2=14+2=14

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