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MAT1308 A INTRODUCTION TO CALCULUS

Assignment 3 due Friday, December 1, 2023 in 11:30 PM

QUESTIONS

Q1. [4 pts] Evaluate the following about the function , and then use that information to sketch its graph.

(1) On what interval(s) is f(x) increasing/decreasing?

(2) On what interval(s) is f(x) concave up/down?

Using all the information you have obtained, sketch the graph of f(x).

Q2. [2 pts] A ladder is leaning against a wall. The ladder is 50 feet long. The bottom of the ladder is being pulled away from the wall at a rate of 10 ft/sec. How fast is the top of the ladder sliding down the wall at the instant when the base of the ladder is 30 feet from the wall?

3. [10 pts] Evaluate the following integrals, showing all your steps:

3.(a)   

3.(b)   

3.(c)   

3.(d)   

3. (e)   

4. [6 pts] Let g(x) = −x2 + 3x + 11 and let h(x) = x2 − 3x + 3.

4.(a) Find the coordinates of the points of intersection of the graphs of g(x) and h(x).

4.(b) On the same axes, sketch the graphs of both g(x) and h(x), clearly labelling the coordinates of their points of intersection. Shade the region(s) bounded between the graphs of g(x) and h(x).

4.(c) Write the definite integral(s) that correspond to the area(s) shaded in part (b).

4.(d) Calculate the exact area of the region(s) bounded between g(x) and h(x).

5. [1 pts Bonus] Just put your answer below