Question

Find the relative extreme values of the function. (If an answer does not exist, enter DNE.)

* f*(

relative max:

relative min:

Answer #1

Find the relative extreme values of the function. (If an answer
does not exist, enter DNE.)
f(x, y) = 3xy − 2x2 − 2y2 + 42x − 21y −
6
relative maximum
relative minimum

Consider the following function. (If an answer does not exist,
enter DNE.)
f(x) = 1 +
5
x
−
3
x2
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up. (Enter your
answer using interval notation.)
(e) Find the interval where the function is concave down. (Enter
your answer using interval notation.)
(f) Find the inflection point.
(x, y) =

Find the limit, if it exists. (If an answer does not exist,
enter DNE.)
lim (x, y)→(0, 0)
x2 + y2/square root (x2 +
y2+ 25)-5

Consider the following. (If an answer does not exist, enter
DNE.)
f '(x) =
x2 + x − 30
(a)
Find the open intervals on which f ′(x) is
increasing or decreasing. (Enter your answers using interval
notation.)
increasing
(−12,∞)
decreasing
(−∞,−12)
(b)
Find the open intervals on which the graph of f is
concave upward or concave downward. (Enter your answers using
interval notation.)
concave upward
concave downward
(c)
Find the x-values of the relative extrema of
f. (Enter...

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

Find (without using a calculator) the absolute extreme values of
the function on the given interval. f(x) = x3 − 12x2 + 21x + 9 on
[−1, 2] absolute min .. Your answer absolute max ..

Find the relative extrema, if any, of the function. Use the
Second Derivative Test if applicable. (If an answer does not exist,
enter DNE.)
g(x) = x3 − 15x
(a) relative maximum (x,y) = ____
(b) relative minimum (x,y) = ____

Consider the equation below. (If an answer does not exist, enter
DNE.)
f(x) =
x4 − 8x2
+ 7
(b) Find the local minimum and maximum values of f.
(c) Find the interval on which f is concave up. (Enter
your answer using interval notation.)
(d) Find the interval on which f is concave down.(Enter
your answer using interval notation.)

Find all relative extrema of the function. Use the
Second-Derivative Test when applicable. (If an answer does not
exist, enter DNE.)
f(x) = x4 − 4x3 + 7
relative maximum
(x, y)
=
relative minimum
(x, y)
=

Consider the equation below. (If an answer does not exist,
enter DNE.)
f(x) = x^7ln(x)
(a) Find the interval on which f is increasing. (Enter your
answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer
using interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c) Find the inflection point.
(x, y) =
Find the interval on which f is concave up....

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