Best solutions to - "What is the average rate of change of..."

Cazzaoro0w9

Answered question

2022-04-17

What is the average rate of change of the function

g (t) = {(t + 2)}^{2}

on the interval [t-h, t]?

resacarno4u

Beginner2022-04-18Added 12 answers

The average rate of change of a continuous function,
f(x), on a closed interval [a,b] is given by

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

So the average rate of change of the function

g (t) = {(t + 2)}^{2}

on [t-h, t] is:

\overset{―}{g} = \frac{g (t) - g (t - h)}{t - (t - h)}

= \frac{{(t + 2)}^{2} - {(t - h + 2)}^{2}}{t - t + h}

= \frac{(t^{2} + 4 t + 4) - (t^{2} + h^{2} - 2 h t - 4 h - 4 t + 4)}{h}

= \frac{t^{2} + 4 t + 4 - t^{2} - h^{2} + 2 h t + 4 h + 4 t - 4}{h}

= \frac{8 t - h^{2} + 2 h t + 4 h}{h}

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