Question

Given the function h(x)=-x^2+4x+12h(x)=−x
2
+4x+12, determine the average rate of change of the function over the interval -2\le x \le 4−2≤x≤4.

Answer 1

SOLUTION

GIVEN

Given the function h(x) = - x² + 4x + 12

TO DETERMINE

The average rate of change of the function over the interval − 2 ≤ x ≤ 4

EVALUATION

Here the given function is

$\displaystyle \sf{ h(x) = - {x}^{2} + 4x + 12 }$

Now the given interval is − 2 ≤ x ≤ 4

Now we have

$\displaystyle \sf{ h( - 2) }$

$\displaystyle \sf{= - {( - 2)}^{2} + (4 \times - 2) + 12 }$

$\displaystyle \sf{= - 4 - 8+ 12 }$

$\displaystyle \sf{=0 }$

Again

$\displaystyle \sf{h(4) }$

$\displaystyle \sf{= - {4}^{2} + (4 \times 4) + 12 }$

$\displaystyle \sf{= - 16 + 16 + 12 }$

$\displaystyle \sf{= 12 }$

Hence the required average rate of change of the function over the interval − 2 ≤ x ≤ 4

$\displaystyle \sf{ = \frac{h(4) - h( - 2)}{4 - ( - 2)} }$

$\displaystyle \sf{ = \frac{12 - 0}{4 + 2} }$

$\displaystyle \sf{ = \frac{12}{6} }$

$\displaystyle \sf{ =2}$

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