Problem 2
Find the locations and values for the maximum and minimum of f
(x, y) = 3x^3 − 2x^2 + y^2 over the region given by x^2 + y^2 ≤
1.
and then over the region x^2 + 2y^2 ≤ 1.
Use the outline:
INSIDE
Critical points inside the region.
BOUNDARY
For each part of the boundary you should have:
• The function g(x, y) and ∇g
• The equation ∇f = λ∇g
• The set of three equations...
1. Find the derivative.
f(x) = x6 ·
3x
2. Find the absolute maximum and
minimum values on the closed interval [-1,8] for the function
below. If a maximum or minimum value does not exist, enter
NONE.
f(x) = 1 − x2/3
3. Find the derivative.
f(x) = x5 ·
e6x
Consider the following.
f(x) = -19ln(84x)
Compute f '(x), then find the exact value of
f ' (3).
Find the absolute maximum and absolute minimum values of
f on the given interval.
f(x) = x3 − 5x + 8, [0, 3]
absolute minimum value
absolute maximum value
Find the absolute maximum and absolute minimum values of
f on the given interval.
f(x) = 4x3 −
6x2 − 144x +
5,
[−4, 5]
absolute minimum
absolute maximum
1. a. Find the relative maximum and minimum values of f(x, y) =
(3x^2) − (2y^2) b. Find the relative maximum and minimum values of
f(x, y) = (x^3) + (y^3) − 6xy . The expression that you may need D
= fxx(x0,
y0)fyy(x0, y0) −
(fxy(x0, y0))2