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Chapter 2: Q. 39 (page 184)

Use the definition of the derivative to find f' for each function f.

f(x)=-2x2

Short Answer

Expert verified

f'(x)=-4x

Step by step solution

01

Step 1. Given information. 

We have been given a function:

f(x)=-2x2

We have to find f' using the definition of the derivative.

02

Step 2. Find the derivative

Derivative of the function can be found as :

limh鈫�0鈥�f(x+h)鈭�f(x)h=limh鈫�0鈥�鈭�2(x+h)2鈭�鈭�2x2h=limh鈫�0鈥�鈭�2x2+2xh+h2+2x2h=limh鈫�0鈥�鈭�4xh鈭�2h2h=limh鈫�0鈥�h(鈭�4x鈭�2h)h=limh鈫�0鈥�鈭�4x鈭�2h=鈭�4x

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