Question

Find the exact location of all the relative and absolute extrema
of the function. HINT [See Example 1.] (Order your answers from
smallest to largest *x*.)

g(x) = 4x^{3} − 12x + 6 with domain [−2, 2]

Answer #1

Find the exact location of all the relative and absolute extrema
of the function. HINT [See Examples 1 and 2.] (Order your answers
from smallest to largest t.)
h(t) = 58t3 + 87t2 with domain [−2,
+∞)
h has ____________________ (t, y) =
h has ____________________ (t, y) =
h has ____________________ (t, y) =
Choices:
Absolute minimum
Absolute maximum
Relative minimum
Relative maximum
No extremum

Find the absolute extrema of the given function on the indicated
closed and bounded set R. (Order your answers from
smallest to largest x, then from smallest to largest
y.)
f(x, y) = x2 + y2 − 2y +
1 on R = {(x, y)|x2 +
y2 ≤ 81}

Find the absolute extrema of the function on the closed
interval. (Order your answers from smallest to largest x,
then from smallest to largest y.)
f(x) = sin(4x), [0, π]
minimum(x, y)=
(x, y)=
maximum(x, y)=
(x, y)=

Find the absolute extrema of the given function on the indicated
closed and bounded set R. (Order your answers from
smallest to largest x, then from smallest to largest
y.)
f(x, y) =
x3 − 9xy −
y3 on R
= {(x, y): −4 ≤
x ≤ 4, −4 ≤ y ≤ 4}

Find all relative extrema of the function. (Be sure to give the
exact coordinates of each and classify as relative minimum or
maximum.)
f(x) = 2x^3 + 4x^2 + 3

Find the absolute extrema if they exist, as well as all values
of x where they occur, for the function:
f(x) = 2x^4 - 100x^2 - 5 ; on the domain [ -6 , 6 ]

Find the absolute extrema if they exist, as well as all values
of x where they occur, for the function:
f(x) = x + e^3x ; on the domain [-3 , 2]

Find all relative extrema of the function. Use the
Second-Derivative Test when applicable. (If an answer does not
exist, enter DNE.)
f(x) = x4 − 4x3 + 7
relative maximum
(x, y)
=
relative minimum
(x, y)
=

Find the absolute extrema if they exist, as well as all values
of x where they occur, for the function:
f(x) = 2x^3 - 48 ln x ; on the domain [ 1 , 5 ]

find the absolute extrema if they exist, as well as all values
of x where they occur, for the function f(x)=x+e^(-3x) on the
domain [-3,3]

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