## Answers

a)

we are given derivative (rate of change of temp) graph and we know that there is relative maxima when derivative changes from positive to negative.

Here derivative changes from positive (above x axis) to negative(below x axis) at t=4. So there is local maxima at t=4

b)

Temp. graph would be concave down when rate of change is decraesing because then second derivative of tem graph would be negative .

And we see that derivative graph is decreasing from t=2 to 2=5

So temp graph is concave down on interval

c)

If we need to find temp. from derivative graph then we need to find area under the derivative graph for that particular time.

We see that area under the curve for interval 0<t<2 is less than the area under the curve for interval 0<t<8.

That means temp at time t=8 is **hotter than** the temp at t=2