Question

grade 12 calculus please help with question 3. i) ?image attached much appreciated

Answer 1

We have a height function

$h(t)=-16t²+96t+112$

Now, to find the average rate of change the height function on [1,3] seconds we have the following

$A_{\lbrack1,3\rbrack}=\frac{h(3)-h(1)}{3-1}=\frac{-16(3)^2+96(3)+112-(-16(1)^2+96(1)+112)}{3-1}=\frac{-16(-8)+96(2)}{2}$

Then the average rate on [1,3] is given by

$A_{\lbrack1,3\rbrack}=\frac{320}{2}=160$

Then the average rate of change of the height function on the interval from 1 to 3 seconds is 160 meters