Question

(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

Answer #1

Consider the function f(x)=x^7e^4x, −4≤x≤3. The absolute maximum
value is and this occurs at x equals The absolute minimum value is
and this occurs at x equals

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 =

consider the function f(x)=x^4-18x^2+9 and find the
absolute maximum and absolute minimum if -2</=x</=-7

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.

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 maximum value and the absolute minimum value of the
function f(x)=x^2-(1/x) on the interval [-2.25,-0.25]

Find the absolute maximum and minimum of f(x,y)=5x+5y with the
domain x^2+y^2 less than or equal to 2^2
Suppose that f(x,y) = x^2−xy+y^2−2x+2y with
D={(x,y)∣0≤y≤x≤2}
The critical point of f(x,y)restricted to the boundary of D,
not at a corner point, is at (a,b)(. Then a=
and b=
Absolute minimum of f(x,y)
is
and absolute maximum is .

(1 point) The function f(x)=3x+5x^−1 has one local minimum and
one local maximum.
This function has a local maximum at x= _____with value______
and a local minimum at x= ______with value_____

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}

The function
f(x,y)equals=8 x squared plus y squared
has an absolute maximum value and absolute minimum value subject
to the constraint
x squared plus 7 y plus y squared=44.
Use Lagrange multipliers to find these values.

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