# Calculus 1 assignment

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 ‘ = 𝑥2 − 𝑥 − 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 𝑓(𝑥) = 𝑥

𝑥 + 1 is increasing at every open interval of its domain.

4. Use L’Hopital Rule to find the limit

lim 𝑥→4

sin2(𝜋𝑥)

𝑒𝑥−4+3−𝑥

5. Find the integral ∫( 5

𝑥2 +

2

𝑥2+1 + sin 𝑥)𝑑𝑥