Math 1210-001
Homework 5
Due 24 June, 2013
This homework assignment is designed to go along with sections 3.1 through
3.3 of your textbook, which we have completed in class. Make sure your work
is neat, legible, well-organized and self-explanatory. You must staple your
assignment to receive full credit.
Name:
1. (10 points) Identify the critical points and find the maximum and minimum of the function f (x) = x3 − 6x2 + x + 2 on the interval [−1, 5].
2. (10 points) Determine where the graph of g(x) is increasing, decreasing, concave up,
and concave down. Find all points of inflection. Then sketch the graph of g(x).
√
g(x) = x x − 2
3. (10 points) Sketch a graph of a function which is differentiable, has domain [0, 6], and
has three local maxima and two local minima on (0, 6). If it is impossible to graph such
a function, indicate this and justify your answer.