Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

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Answer #1

Find the critical numbers of the function. (Enter your answers
as a comma-separated list. If an answer does not exist, enter
DNE.)
f(x) = x3e−7x
Find the absolute maximum and absolute minimum values of
f on the given interval.
f(x) = x3 − 6x2 + 9x +
6, [−1, 4]

Find the critical numbers of the function. (Enter your answers
as a comma-separated list. If an answer does not exist, enter
DNE.)
g(t) = |2t − 1|
t =

Find the critical numbers of the function. (Enter your answers
as a comma-separated list. Use n to denote any arbitrary
integer values. If an answer does not exist, enter DNE.)
f(θ) = 4 cos(θ) + 2 sin2(θ)

1. Consider the following.
h(x)=x 3sqrt(x-5)
Find the critical numbers. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
x =
Find the open intervals on which the function is increasing or
decreasing. Use a graphing utility to verify your results. (Enter
your answers using interval notation. If an answer does not exist,
enter DNE.)
increasing:
decreasing:
2. Compare the values of dy and Δy for the
function. (Round your answers to four decimal...

a. Find the critical numbers of the function on the interval ( 0
, 2 π ) . (Enter your answers as a comma-separated list. If an
answer does not exist, enter DNE.) g(θ)=8θ−2tanθ
b. If a and b are positive numbers, find the maximum value of f
( x ) = x^a(4−x)^b on the interval 0 ≤ x ≤ 4

Find the local maximum and minimum values and saddle point(s) of
the function. (Enter your answers as a comma-separated list. If an
answer does not exist, enter DNE.)
f(x, y) =
x3 + y3 −
3x2 − 3y2
− 9x

Consider the function below.
f(x) = 7 + 4x2 − x4
(a) Find the interval of increase. (Enter your answer using
interval notation.)
(b) Find the interval of decrease. (Enter your answer using
interval notation.)
(c) Find the local minimum value(s). (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
(d) Find the local maximum value(s). (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)

2). Find the asymptotes of the hyperbola. (Enter your answers as
a comma-separated list of equations.)
y2 − 9x2 − 2y +
18x = 89
3). Find the asymptotes of the hyperbola. (Enter your answers as
a comma-separated list of equations.)
16x2 − 9y2 = 144

Find the local maximum and minimum values and saddle point(s) of
the function. If you have three-dimensional graphing software,
graph the function with a domain and viewpoint that reveal all the
important aspects of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
f(x, y) = 5 − x4 + 2x2 − y2

Find all rational zeros of the polynomial. (Enter your answers
as a comma-separated list. Enter all answers including
repetitions.)
P(x) = 8x^3 + 10x^2 − x − 3
write the polynomial in factored form.

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