Understanding Functions and Their Derivatives Graphically
A function appears in the SageMath plot below. Its tangent line at the point \(x = c\) is plotted in red. As you move the slider, the SageMath plot displays the coordinates of the point \((c, f(c))\) and the equation of the tangent line at \(x = c\). Use the SageMath plot to answer the questions in the exercise.
3. The temperature inside a house (in degrees Fahrenheit) is plotted as a function of \(t\), the number of hours elapsed since midnight. Be sure to include units with all of your answers in your lab report.
(a) What is the temperature of the house at the time specified in your lab report?
(b) How fast is the temperature of the house changing at the time specified in your lab report? Attach a printout of the plot you based your answer on to your lab report.
(c) By how much did the temperature change between the times specified in your lab report?
(d) What was the average rate at which the temperature changed between the two times specified in your lab report?