Question

what is the average rate of change of the function h(x) = 6 - 3x² on the interval from x = -2 to x = 1?

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function \( h(x) \) on the interval \([a, b]\) is given by \(\frac{h(b) - h(a)}{b - a}\). Here, \( a=-2 \) and \( b = 1 \).

Step2: Calculate \( h(-2) \)

Substitute \( x=-2 \) into \( h(x)=6 - 3x^{2} \):

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Step3: Calculate \( h(1) \)

Substitute \( x = 1 \) into \( h(x)=6 - 3x^{2} \):

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Step4: Calculate the average rate of change

Using the formula \(\frac{h(1)-h(-2)}{1-(-2)}\), substitute \( h(1) = 3 \) and \( h(-2)=-6 \):

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Answer:

\( 3 \)