1. You are given the function f(x) = 3x^4 + 4x^3
a) Find the x and y- intercepts.
b) Find the critical number(s) of f.
c) Find the interval(s) of increase and decrease of f.
d) Find the relative maximum and minimum value(s) of f.
e) Find the hypercritical number(s) of f.
f) Find the interval(s) of upward and downward concavity off.
g) Find the point(s) of inflection of f.
h) Sketch the graph of f.
2. You are given the function f(x) = x/(1−x)
a) Find the x and y- intercepts.
b) Find the horizontal asymptote(s).
c) Find the vertical asymptote(s) and do a limit analysis of thebehavior of f on either
side of each vertical asymptote.
d) Find the critical number(s) of f.
e) Find the interval(s) of increase and decrease of f.
f) Find the relative maximum and minimum value(s) of f.
g) Find the hypercritical number(s) of f.
h) Find the interval(s) of upward and downward concavity off.
I) Find the point(s) of inflection of f.
j) Sketch the graph of f.
3. Find the absolute maximum and absolute minimum of f(x) = x^3− 3x on [0, 3].
4. Why doesn’t the Extreme Value Theorem apply to f(x) =1/x onthe interval [-3, 3]?
