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

Answered: Using the definition, caleuhate the…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

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Chapter3: Functions

Section3.4: Composition Of Functions

Problem 4SE: How do you find the domain for the composition of two functions, fg ?

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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