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Q. 48

Found in: Page 184


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

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


The value of f'(x)=-96x32

See the step by step solution

Step by Step Solution

Step 1. Given information

The given function f(x)=3x

Step 2. Finding the value of f'(x)

We know that f'(x)=limh0f(x+h)-f(x)h .....(1)

Given f(x)=3x

Then f(x+h)=3x+h

Putting these values in (1)

f'(x)=limh03x+h-3xh =limh03x-3x+hxx+hh =limh03x-3x+hxx+h×3x+3x+h3x+3x+hh =limh0(3x)2-(3x+h)2xx+h(3x+3x+h)h =limh09x-9x-9hxx+h(3x+3x+h)h =limh0-9hxx+h(3x+3x+hh =limh0-9xx+h(3x+3x+h)

Putting h=0


Hence,the value of f'(x)=-96x32

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