Question

Let f(x, y) = 2x 3 − 6xy + y 2 − 4. Find all local minima, local maxima, and saddle points of f(x, y).

Answer #1

f(x,y)=x2+xy+y2+2x-5y+5 Find the local
Maximum(?,?). The local maximum value is/are (?)Find all the local
maxima, local minima, and saddle points of the function

(5) Let f(x, y) = −x^2 + 2x − 3y^3 + 6y^2 − 3y.
(a) Find both critical points of f(x, y).
(b) Compute the Hessian of f(x, y).
(c) Decide whether the critical points are saddle-points, local
minimums, or local maximums.

Suppose f(x,y)=(x-y)(1-xy)
Find the following a.) The local maxima of f
b.) The local minima of f
c.) The saddle points of f

Find the local maximum and minimum values and saddle point(s) of
the function f ( x , y ) = f(x,y)=xe^(-2x2-2y2). If there are no
local maxima or minima or saddle points, enter "DNE."
The local maxima are at ( x , y ) = (x,y)= .
The local minima are at ( x , y ) = (x,y)= .
The saddle points are at ( x , y ) =

Let f(x)=6x^2−2x^4. Find the open intervals on which f is
increasing (decreasing). Then determine the x-coordinates of all
relative maxima (minima).
1.
f is increasing on the intervals
2.
f is decreasing on the intervals
3.
The relative maxima of f occur at x =
4.
The relative minima of f occur at x =

Find the local maxima and minima values for the function f(x)=
e^(x^5-x^4-2x^3+x^2-1)

f (x, y) =(x ^ 4)-8(x ^ 2) + 3(y ^ 2) - 6y
Find the local maximum, local minimum and saddle points of the
function.
Calculate the values of the function at these points

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

what does a derivative tell us?
F(x)=2x^2-5x-3, [-3,-1]
F(x)=x^2+2x-1, [0,1]
Give the intervals where the function is increasing or
decreasing?
Identify the local maxima and minima
Identify concavity and inflection points

(3)If H(x, y) = x^2 y^4 + x^4 y^2 + 3x^2 y^2 + 1, show that H(x,
y) ≥ 0 for all (x, y). Hint: find the minimum value of H.
(4) Let f(x, y) = (y − x^2 ) (y − 2x^2 ). Show that the origin
is a critical point for f which is a saddle point, even though on
any line through the origin, f has a local minimum at (0, 0)

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