Math 2413 Written Assignment 3 Name_________________________________________
Present all of your work in your own handwriting in the space provided for each problem. Problems
asking you to write out answers to questions require full sentences. The word problems also require a
full sentence response. Grammar, capitalization, and punctuation all count, along with the answer being
correct.
1. The 800-room Mega Motel is filled to capacity when the charge is $50 per night. For each $10
increase in room charge 40 fewer rooms are filled each night. What charge per room will result in the
maximum revenue per night. (Use Calculus to solve the problem)
2. Suppose y β = π₯2 β π₯ β 6 is the first derivative of the function y = f(x).
a) At what points, if any, does the graph of f have a local maximum, minimum, or inflection points?
b) Find the intervals where the function is increasing, decreasing, concave up, or concave down and
sketch a general shape of the graph.
Math 2413 Written Assignment 3 Name_________________________________________
3. Show that the function π(π₯) = π₯
π₯ + 1 is increasing at every open interval of its domain.
4. Use LβHopital Rule to find the limit
lim π₯β4
sin2(ππ₯)
ππ₯β4+3βπ₯
5. Find the integral β«( 5
π₯2 +
2
π₯2+1 + sin π₯)ππ₯
