Discuss the below:
Q1. Let f(x)=0.112x3=1.8x2+4x+41 be a function that models the temperature change in a certain valley from 6:00 PM one day to 8:00 AM the following morning. Let the origin represent the temperature at 6:00 pm.
a. Find, and then sketch, the first and second derivatives of f(x)=0.112x3=1.8x2+4x+41 on the grids above. Label the axes and mark the scales (unit size) on each axis. Use the same domains in each case.
b. What point(s) on the first derivative graph correspond to the turning points (the max and the min) on the original function? State the x values of the points. What clock time(s) do the x values represent, to the nearest minute?
c. What point(s) on the second derivative graph correspond to the change in concavity (the inflection point) of the function? Hint: where is the first derivative a max or a min? State the x value(s) of the point(s).
d. What is the significance of the inflection point? To answer this, simply fill in the blank and circle the appropriate answers: "The inflection point is where the rate of change is at a ____________________. Thus the temperature was increasing/decreasing at its greatest/slowest rate."
Q2. The marginal revenue function for a popular software company (see sample of their work to the right) is R(x)=3.5x+15 where x is sales in hundreds and marginal revenue is in thousands of dollars.
a. Find the original revenue function R(x) using the antiderivative. Assume that when the company first started, at "time zero", the revenue was zero.
b) What is the revenue from sales that total 150 hundred units?