At 7:00 AM, the temperature was 30 degrees; 3 hours later it was 42 degrees. Assuming the temperature function is differentiable, what can be concluded from the Mean Value Theorem? Don't assume the temperature increased at a constant rate.

Question

I know that Mean Value Theorem is f'(c)=f(b)-f(a)/b-a, but I'm not sure how to apply it to this problem.

Answer 1

The temperature rose 12 degrees in 3 hours.
That is a mean rate of change of 4°/hr
So, somewhere in that interval the tangent to the temperature curve has a slope of 4