Find the averags vaha of change ef -+2over achof malta) From 2 toD) From to 2{e) Fiem 0 ta 3ta) The average rate ofhange from 2to 4

Answered: Find the averags vaha of change ef…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Find the averags vaha of change ef -+2over achof mal
ta) From 2 to
D) From to 2
{e) Fiem 0 ta 3
ta) The average rate ofhange from 2to 4

Expert Solution

Step 1

Given function is $f (x) = - 2 x^{2} + 2$ .

To find: The average rate of change of function over the given intervals.

(a) From 2 to 4.

(b) From 0 to 2.

Solution:

The average rate of change of a function $f (x)$ from $a$ to $b$ is given as:

$A (x) = \frac{f (b) - f (a)}{b - a}$

Step 2

The average rate of change of $f (x)$ from 2 to 4 will be:

$\begin{array}{rcl} A (x) & = & \frac{f (4) - f (2)}{4 - 2} \\ = & \frac{[- 2 {(4)}^{2} + 2] - [- 2 {(2)}^{2} + 2]}{4 - 2} \\ = & \frac{[- 2 \cdot 16 + 2] - [- 2 \cdot 4 + 2]}{2} \\ = & \frac{[- 32 + 2] - [- 8 + 2]}{2} \\ = & \frac{- 30 + 6}{2} \\ = & \frac{- 24}{2} \\ = & - 12 \end{array}$