Question

Verify that the function
f(x)=(1/3)x^{3}+x^{2}−3x attains an absolute
maximum and absolute minimum on [0,2]. Find the absolute maximum
and minimum values for f(x) on [0,2].

Answer #1

For the function , (1)/(3)x^(3)-3x^(2)+8x+11
1)at x=, f(x) attains a local maximum value of
f(x)
2)at x=, f(x) attains a local minimum value of f(x)

dentify the absolute minimum and absolute maximum values of the
function f(x)=x3−12x2−27x+22 f ( x ) = x 3 - 12 x 2 - 27 x + 22 on
the interval [−2,4]

Find the absolute maximum value and the absolute minimum value
of the function f(x,y)=(1+x2)(1−y2) on the disk
D={(x,y) | x2+y2⩽1}

Find the absolute maximum, and minimum values of the function:
f(x, y) = x + y − xy Defined over the closed rectangular region D
with vertices (0,0), (4,0), (4,2), and (0,2)

Find the absolute maximum and absolute minimum values of
f(x)=x3+3x2−9x+1 on [-5,-1] , along with
where they occur.
The absolute maximum value is ? and occurs when x is ?
the absolute minimum value is ? and occurs when x is ?

For the function ?(?)=?⋅e^(e^x-x^2)", find the absolute maximum
and absolute minimum over the domain [0,2].

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 − x^2/3
Find the absolute maximum and absolute minimum values of the
function below. If an absolute maximum or minimum does not exist,
enter NONE.
f(x) = x3 - 12x on the
closed interval [-3,5]

Find the absolute maximum and minimum for
f(x)=x3-12x+1 in [-3,5]

1. Find the absolute maximum value and the absolute minimum
value, if any, of the function. (If an answer does not exist, enter
DNE.)
g(x) =
−x2 + 4x + 9
maximum =
minimum=
2. Find the absolute maximum value and the absolute minimum
value, if any, of the function. (If an answer does not exist, enter
DNE.)
f(x) = x2 − x − 3 on [0, 3]
3.
Find the absolute maximum value and the absolute minimum value,
if...

(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...

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