CALCULUS
REVIEW 3.1 – 3.6
NAME: _______________________
DATE: ________________________
1. Find the extrema of f(x) = 6x4 – 8x3 on the interval [-1, 2].
2. State whether the Mean Value Theorem applies and why. If yes, find all values of c in
f (b) − f (a )
(a, b) such that: f ’(c) =
b−a
a.) f(x) = cos 2x
[0, 2π]
b.) f(x) = tan 2x
[0, π]
c.) f(x) = x(x2 + x + 4) [-1, 1]
3. State whether Rolle’s Theorem can be applied on the indicated interval. If yes, find all
values of c in (a, b) such that: f ’(c) = 0.
a.) f (x) = x − 2
⎡ 1 1⎤
⎢⎣ − 2 , 2 ⎥⎦
⎛ x⎞
b.) f (x) = tan ⎜ ⎟
⎝ 3⎠
[ 0, 2π ]
c.) f (x) = (2x − 6)(x + 1)2
[ −1, 3]
4. Curve Sketching. Complete the curve sketching template for the following:
a.) f (x) = (x − 1)(x − 3)
2
x −1
b.) f (x) =
x+3
2x 2 + 1
c.) f (x) =
x−2
5. The function f drawn below would be difficult to describe algebraically; nevertheless, it has
interesting geometric features for which calculus provides descriptions. Name the
value(s) for x for:
a.) zero(s) of f(x) __________________________________________
b.) points of discontinuity of f _________________________________
c.) critical points ___________________________________________
d.) intervals over which f increases ____________________________
e.) intervals over which f decreases ___________________________
f.) relative maxima ________________________________________
g.) relative minima _________________________________________
h.) intervals over which f is concave up _________________________
i.) intervals over which f is concave down _______________________
j.) points of inflection _______________________________________
k.) equation(s) of any horizontal asymptotes _______________________
l.) equation(s) of any vertical asymptotes _________________________