Q1: Using the definition, caleuhte the derivative of the followng function.f (x) = 4-x²

Answered: Using the definition, caleuhate the…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 2E

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Q1: Using the definition, caleuhte the derivative of the followng function.
f (x) = 4-x²

Expert Solution

Step 1

Derivative:

A function is said to be derivable or differentiable if

$\lim_{∆ x \to 0} \frac{f (x + ∆ x) - f (x)}{∆ x}$ exists and this limit is denoted as $f' (x)$ or $\frac{d f}{d x}$ .

$D$ or $\frac{d}{d x}$ is called the differential operator.

Hence

$f' (x) = \lim_{∆ x \to 0} \frac{f (x + ∆ x) - f (x)}{∆ x}$ is called the derivative of $f (x)$ .

The process of finding derivatives is called differentiation.

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Using the definition, caleuhate the derivative of the following function. f (x) = 4-x²