Question

1. The absolute maximum value of f(x) = x 3 − 3x 2 + 12 on the interval [−2, 4] occurs at x =? Show your work.

2.t. Let f(x) = sin x + cos2 x. Find the absolute maximum, and absolute minimum value of f on [0, π]. Show your work.

Absolute maximum:

Absolute minimum:

3.Let f(x) = x √ (x − 2). The critical numbers of f are_______. Show your work.

Answer #1

(a) Find the maximum and minimum values of f(x) = 3x 3 − x on
the closed interval [0, 1] by the following steps:
i. Observe that f(x) is a polynomial, so it is continuous on the
interval [0, 1].
ii. Compute the derivative f 0 (x), and show that it is equal to
0 at x = 1 3 and x = − 1 3 .
iii. Conclude that x = 1 3 is the only critical number in...

Find the absolute maximum and absolute minimum values of f on
the given interval. f(x) = 3x^2 − 18x + 8, [0, 8] absolute minimum
value.

Find the absolute maximum and minimum values of f(x)=
−x^3−3x^2+4x+3, if any, over the interval
(−∞,+∞)(−∞,+∞).
I know it doesn't have absolute maxima and minima but where do
they occur? In other words x= ? for the maxima and minima?

Consider the function
f(x)=3−7x2, −3≤x≤2
The absolute maximum value is
and this occurs at x=
The absolute minimum value is
and this occurs at x =

1. If f (x)= ln(3x^2 -2x +9), find the absolute minimum and
absolute maximum on [-2,2]
.

Find the absolute minimum and maximum on the interval [0, 3]
for: f(x) = x^2 − 5x

Find the absolute maximum value and the absolute minimum value
of the function f ( x , y ) = x 2 y 2 + 3 y on the set D defined as
the closed triangular region with vertices ( 0 , 0 ), ( 1 , 0 ),
and ( 1 , 1 ), that is, the set D = { ( x , y ) | 0 ≤ x ≤ 1 , 0 ≤ y
≤ x }...

Find the absolute maximum and absolute minimum values of f on
the given interval: x^4-8x^2+8 [-3, 4]
Absolute minimum:
Absolute maximum:

(1 point) Consider the function f(x)=2−5x^2,−4≤x≤2
The absolute maximum value is
and this occurs at x equals
The absolute minimum value is
and this occurs at x equals

Find the absolute minimum and absolute maximum of
f(x,y)=10−3x+8y
on the closed triangular region with vertices (0,0),(8,0) and
(8,12).
List the minimum/maximum values as well as the point(s) at which
they occur. If a min or max occurs at multiple points separate the
points with commas.

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