For the function f(x,y) = 4xy - x^3 - 2y^2 find and label any
relative extrema or saddle points. Use the D test to classify. Give
your answers in (x,y,z) form. Use factions, not decimals.
Find the coordinates of all local extrema and inflections of y =
x − 4√x. Give the intervals where the function is increasing,
decreasing, concave up, and concave down.
The derivative of a function is f'(x)=-6x^2(x-1)(x+2). How can I
identify any local extrema of f, if any? How can use the First
Derivative test to determine if any of the local extreme identified
are a relative maximum or a relative minimum?
1. Find the local maxima of the function:
(1) f(x,y) = xy, subject to the constraint that
x+y-1=0. Result should be 1/4.
2. Find the local minima of the functions:
(1) f(x,y) = x^2+y^2, subject to the constraint that
xy-3=0. Result should be 6.
(2) f(x,y) = x^2+4xy+y^2, subject to the constraint
that x-y-6=0. Result should be -18.
For f(x)= cos2x + sinx, find the intervals where the
function is increasing, decreasing, relative extrema, concavity,
and points of inflection on the interval [0,2π)
Consider the following.
optimize f(x,
y) = 5x2 +
4y2 − 25.1x −
11.9y + 73.9
subject to g(x,
y) = 4x + y =
7
(b) Locate the optimal point of the constrained system. (Round
all values to three decimal places.)
(x, y,
f(x, y))
=