Chapter 3 Review
1) Consider the graph of the function f(x) below.
a) the open intervals where the function graphed is
increasing
b) the open intervals where the function graph is
decreasing
c) the coordinates of all relative maxima
d) the coordinates of all relative minima
#2-4: For each function find the following:
a) f’(x)
b) the critical numbers
c) the open interval(s) where the function is
increasing
d) the open interval(s) where the function is
decreasing
e) the coordinates of all relative maxima
f) the coordinates of all relative minima
2) 𝑓 (𝑥 ) = 𝑥 3 − 75𝑥
#2-4: For each function find the following:
a) f’(x)
b) the critical numbers
c) the open interval(s) where the function is
increasing
d) the open interval(s) where the function is
decreasing
e) the coordinates of all relative maxima
f) the coordinates of all relative minima
3) 𝑓 (𝑥 ) =
𝑥 2 −6𝑥+9
𝑥−5
#2-4: For each function find the following:
a) f’(x)
b) the critical numbers
c) the open interval(s) where the function is
increasing
d) the open interval(s) where the function is
decreasing
e) the coordinates of all relative maxima
f) the coordinates of all relative minima
4) 𝑓 (𝑥 ) = 𝑥𝑒 𝑥
5) Consider the graph of the function f(x) below.
a) Find the open intervals where the function is
concave upward or downward.
b) Find all inflection points
6) 𝑓 (𝑥 ) = 𝑥 3 − 12𝑥 2 + 7
a) Find the open intervals where the function is
concave upward or downward.
b) Find all inflection points
#7-8: Find the following.
a) Find the domain
b) Find the x-intercept(s), if any
c) Find the y-intercept, in there is one
d) Find the interval(s) where the graph of the
function is increasing
e) Find the interval(s) where the graph of the
function is decreasing
f) Find all relative maxima and relative minima
g) Find the interval(s) where the graph of the
function is concave up (if any)
h) Find the interval(s) where the graph of the
function is concave down (if any)
i) Find all inflection points (if any)
j) Sketch a graph
7) f(x) = x3 – 3x2
#7-8: Find the following.
a) Find the domain
b) Find the x-intercept(s), if any
c) Find the y-intercept, in there is one
d) Find the interval(s) where the graph of the
function is increasing
e) Find the interval(s) where the graph of the
function is decreasing
f) Find all relative maxima and relative minima
g) Find the interval(s) where the graph of the
function is concave up (if any)
h) Find the interval(s) where the graph of the
function is concave down (if any)
i) Find all inflection points (if any)
j) Sketch a graph
8) f(x) = 4xex
#9) Find the following.
a) Find the domain and vertical asymptotes
b) Find the x-intercept(s), if any
c) Find the y-intercept, in there is one
d) Find all vertical asymptotes
e) Find the interval(s) where the graph of the
function is increasing
f) Find the interval(s) where the graph of the
function is decreasing
g) Find all relative maxima and relative minima
h) Find the interval(s) where the graph of the
function is concave up (if any)
i) Find the interval(s) where the graph of the
function is concave down (if any)
j) Find all inflection points (if any)
k) Sketch a graph
9) 𝑓 (𝑥 ) =
𝑥−2
𝑥+3
10) A headphone determines that in order to sell x
units of a new headphone, the price demand
equation for the headphones is given by
p = 500 − x.
It also determines that the total cost of producing x
units is given by C(x) = 2000 − 20x .
a) Create a revenue function.
b) Create a profit function.
c) How many units must the company produce and
sell to maximize profit?
d) What is the maximum profit?
e) What price per unit must be charged to make
maximum profit?