Question

Find the local extrema of the following function. f(x,y) =
x^{3}-3xy^{2}+15y^{2}

Answer #1

find the local extrema of hte function f(x)= sin2x on [0,pi]

Find the intervals of increase and decrease as well as the local
extrema for the function
f(x)=x3(x−5)2.
Compute the limit.
lim x→0
2cos(4x)−4x2−2
sin(2x)−x2−2x

Use analytical methods to find all local extrema of the function
f(x)=3x^1/x for x>0.
The function f has an absolute maximum of ? at x=?
The function f has an absolute minimum of ? at x=?

Find all local extrema for f(x, y) = 2y3 +
18x2 − 36xy.
(If an answer does not exist, enter DNE.)

Solve each equation.
(a) 5·32x−1 = 20
(b) 4x+5/3=x-3/4
2)Find the local extrema of the function
f(x) = x3 −6x2 +4x−2.
3) Find the local extrema of the function f(x) = x3 −6x2
+4x−2.
4) Suppose $5, 000 is invested at 3% annual interest, compounded
monthly.
(a) Write a function that describes the value of the investment
after t years.
(b) How much is the investment worth after 3 years?
(c) When is the investment worth $8, 000?

If f(x,y)=(5∗x3+4∗y3+4∗x∗y+1) find the critical point for
f(x,y)
x=____
y=____
Is this critical point a local maximum, local minimum, or saddle
point?

For f(x) xe-x
( a) Find the local extrema by hand using the first derivative
and a sign chart. b) Find the open intervals where the function is
increasing and where it is decreasing. c) Find the intervals of
concavity and inflection points by hand. d) Sketch a reasonable
graph showing all this behavior . Indicate the coordinates of the
local extrema and inflections.

Find the local extrema of the function f(x)=sec2x-2tanx on the
interval -(pi/2)<x<(pi/2), and say where they occur.

Consider the function f(x) = −x3 + 4x2 + 7x + 1.
(a) Use the first and second derivative tests to determine the
intervals of increase and decrease, the
local maxima and minima, the intervals of concavity, and the
points of inflection.
(b) Use your work in part (a) to compute a suitable table of
x-values and corresponding y-values and carefully sketch the graph
of the function f(x). In your graph, make sure to indicate any
local extrema and any...

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) = x3 − 3x + 3xy2

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