Bonus problems for Math 151

On this page I post some bonus problems that may increase your daily grade score (of course, if you solve them). For each problem there is a due date. Each problem is worth 5 points. If you solve the problem by the due date, write the solution down on a separate sheet and bring it to me. We'll talk a little and if I see that you really have correct solution you get you 5 points.

DO NOT COPY THE SOLUTION FROM OTHER PEOPLE. DO THESE PROBLEMS BY YOURSELF. Since I will ask you about the problem, I will understand if you just copied the solution.

So, here are the problems:

1. (a) Solve the inequality |x+1|+|x-2|<7
(b) Sketch the graph of the function y=|x+1|+|x-2|
(c) Where is f continuous?
(d) Where is f differentiable?

This problem is due Thursday, October 12. Remember, if you solve the problem, do not tell anyone the solution!!!

Solution of Bonus Problem 1.

2. Find y' and y'' if
(x²+y)e^cosy=1.

Thank you, Mr. Kulkarni for your remark.

This problem is due Thursday, October 19.

Solution of Bonus Problem 2.

3.(10 pts) Given function f(x)=(x-3)x^1/2.
(a) Find the domain and range of f(x).
(b) Where is f(x)=0, f(x)>0, f(x)<0?
(c) Where is f(x) continuous?
(d) Find the intervals on which f(x) is decreasing or increasing.
(e) Find the local minimum and maximum values of f(x).
(f) Find the intervals of concavity and the inflection points.
(e) Use the information from parts (a)-(f) to sketch the graph of f(x).

This problem is due Thursday, November 2.

Bonus problem 4 you can find here.

This problem is due Thursday, November 9.

And the last one.

5. Find the area of skin of the grey animal in the figure below:

This problem is due Monday, November 20.

This problem is worth 15 points due Thursday, November 16 and 10 points due Monday, November 20.