g(x, y) = 2x 3 + 9xy2 + 15x 2 +
27y2
Find all the critical...
g(x, y) = 2x 3 + 9xy2 + 15x 2 +
27y2
Find all the critical points of the following functions. For
each critical point of g(x, y), determine whether g has a local
maximum, local minimum, or saddle point at that point.
The function f(x, y) = 10−x 2−4y 2+2x has one critical point.
Find that critical point and show that it is not a saddle point.
Indicate whether this critical point is a maximum or a minimum, and
find that maximum or minimum value.
Let f(x,y) = 3x3 + 3x2 y − y3 −
15x.
a) Find and classify the critical points of f. Use any method
taught during the course (the second-derivative test or completing
the square).
b) One of the critical points is (a,b) = (1,1). Write down the
second-degree Taylor approximation of f about this point and
motivate, both with computations and with words, how one can see
from this approximation what kind of critical point (1,1) is. Use
completing the...
Let f(x,y) = 3x3 + 3x2 y − y3 −
15x.
a) Find and classify the critical points of f. Use any method
taught during the course (the second-derivative test or completing
the square).
b) One of the critical points is (a,b) = (1,1). Write down the
second-degree Taylor approximation of f about this point and
motivate, both with computations and with words, how one can see
from this approximation what kind of critical point (1,1) is. Use
completing the...
Consider the region bounded between y = 3 + 2x - x^2 and y = e^x
+ 2 . Include a sketch of the region (labeling key points) and use
it to set up an integral that will give you the volume of the solid
of revolution that is obtained by revolving the shaded region
around the x-axis, using the... (a) Washer Method (b) Shell Method
(c) Choose the integral that would be simplest to integrate by hand
and integrate...
Consider the function f(x, y) = 4xy − 2x 4 − y
2 .
(a) Find the critical points of f.
(b) Use the second partials test to classify the critical
points.
(c) Show that f does not have a global minimum.
1. Find the critical numbers for the following functions
(a) f(x) = 2x 3 − 6x
(b) f(x) = − cos(x) − 1 2 x, [0, 2π]
2. Use the first derivative test to determine any relative
extrema for the given function
f(x) = 2x 3 − 24x + 7