Graph of derivative of temperature as a function of time

Question

A pie is removed from a hot oven and left to cool to room temperature. Sketch a graph of the derivative of the pie’s temperature as a function of time. (You do not need to sketch a graph of the pie’s temperature, but you may find it helpful. If you do, clearly label the graph that is the derivative.)

 

Right now in class we're learning how to sketch graphs of the derivative of a function were the graph is shown but I'm lost on how to even start on this HW problem. Please help

Answer 1

Consider the graph of temperature, over (as a function of) time.

It will be a decreasing function with upward concavity.

Now consider the tangents to that curve, over time.

These slopes are all negative numbers, which INCREASE (becoming less negative).  

Now you can try a representative sketch.