Find the average rate of change of the following function 1)f\left ( x \right )=X^{2} on the...

Question:

Find the average rate of change of the following function

1){eq}f\left ( x \right )=X^{2} {/eq} on the interval {eq}\left [ 1,4 \right ] {/eq}

2){eq}f\left ( x \right )=X^{2}+1 {/eq} on the interval {eq}\left [ 3,7 \right ] {/eq}

3){eq}f\left ( x \right )=X^{2} {/eq}on the interval {eq}\left [ x,x+h \right ] {/eq} for {eq}h\neq 0 {/eq}

Average Rate of Change:

The average rate of change of a function {eq}f(x) {/eq} is the change in the output value divided by the change in the input value.

The average rate of change of {eq}f(x) {/eq} from {eq}x=a {/eq} to {eq}x=b {/eq} is:

{eq}\frac{f\left ( b \right )-f\left ( a \right )}{b-a} {/eq}

Answer and Explanation: 1

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1) The average rate of change of {eq}f\left ( x \right )=X^{2} {/eq} on the interval {eq}\left [ 1,4 \right ] {/eq} is:

{eq}\frac{f\left ( 4...

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Average Rate of Change: Definition, Formula & Examples

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Chapter 20 / Lesson 5
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Finding the average rate of change is similar to finding the slope of a line. Study the definition of average rate of change, its formula, and examples of this concept.


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