Question

g(t)=−(t−1) 2
+5g, left parenthesis, t, right parenthesis, equals, minus, left parenthesis, t, minus, 1, right parenthesis, squared, plus, 5
What is the average rate of change of ggg over the interval -4\leq t\leq 5−4≤t≤5minus, 4, is less than or equal to, t, is less than or equal to, 5?

Answer 1

SOLUTION

TO DETERMINE

The average rate of change of g(t) over the interval - 4 ≤ t ≤ 5

$\sf{g(t) = - {(t - 1)}^{2} + 5}$

EVALUATION

Here the given function is

$\sf{g(t) = - {(t - 1)}^{2} + 5}$

Now

$\sf{g( - 4) }$

$\sf{= - {( - 4- 1)}^{2} + 5 }$

$\sf{= - 25 + 5}$

$\sf{ = - 20}$

Again

$\sf{g( 5) }$

$\sf{ = - {( 5- 1)}^{2} + 5 }$

$\sf{ = - 16 + 5 }$

$\sf{ = - 11}$

Hence the required average rate of change of g(t) over the interval - 4 ≤ t ≤ 5

$\displaystyle \sf{ = \frac{g(5) - g( - 4)}{5 - ( - 4)} }$

$\displaystyle \sf{ = \frac{ - 11 + 20}{5 + 4} }$

$\displaystyle \sf{ = \frac{ 9}{9} }$

$\displaystyle \sf{ = 1}$

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