Question

**1) Find the absolute maximum value and the absolute
minimum, if any, of the given function. f(x) = 2x 3 − 3x 2 − 36x +
5 on [−1, 4]**

**2) A manufacturer of a certain commodity has estimated
that her profit in thousands of dollars is given by the expression
−2x 2 + 14x−6 where x (in thousands) is the number of units
produced. What is the maximum profit the manufacturer could realize
on the commodity?**

Answer #1

1. Find the absolute maximum value and the absolute minimum
value,if any, of each function.
(a) f(x) = -x2+ 4x + 6 on [0, 5]
(b) g(x)= x+1 / x−1 on [2, 4]

Find the absolute maximum and minimum values of the following
function over the indicated interval, and indicate the x-values
at which they occur.
f(x)=1/3x^3+3/2x^2-4x+4 [-5,3]

Find the absolute maximum and absolute minimum values of
f on the given interval.
f(x) = 4x3 −
12x2 − 36x +
6,
[−2, 4]

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

Find the absolute maximum and absolute minimum values, if any,
of the function. (If an answer does not exist, enter DNE.)
h(x) = x3 + 3x2 + 3 on [−3, 2]
absolute maximum ______
absolute minimum _______

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
f(x) = x^4-2x^2+1 [-2,3]

Find the absolute maximum and minimum values of each function
over the indicated interval, and indicate the x-values at which
they occur.
f(x) = 3x^3 - 3x^2 - 3x + 7 ; [-1 , 0]
The absolute maximum value is _ at x = _
(Use a comma to separate answers as needed. Type an integer or
a fraction.)

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 minimum and the absolute maximum of the
function on the interval given. (Round your answers to four decimal
places.)
f(x) = 2xe−x on [0, 4]. (and yes i do mean
^-x)

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