Question

Find the maximum value of y= 1/3x^3 + x^2 - 8x +31/3

Answer #1

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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)

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.

Show that the curve y = 3x^3 + 8x − 2 has no tangent line with
slope 3

Find two positive numbers x and y whose sum is 7 so that
x^(2)*y−8x is a maximum.

1.Find the area of the region between the curves y= x(1-x) and y
=2 from x=0 and x=1.
2.Find the area of the region enclosed by the curves
y=x2 - 6 and y=3 between their
interaction.
3.Find the area of the region bounded by the curves
y=x3 and y=x2 between their interaction.
4. Find the area of the region bounded by y= 3/x2 ,
y= 3/8x, and y=3x, for x greater than or equals≥0.

Find the absolute maximum and minimum of f(x,y)= 3x+4y within
the domain x^2+y^2 less than or equal tp 2^2
Find the points on the cone z^2=x^2+y^2 that are closest to the
point (3,4,0)

Find the maximum product of two numbers x and y subject to 3x +
4y = 3. Hint: Use Lagrange multipliers.

1) Find the arclength of y=4x+3 on 0≤x≤3
2) Find the arclength of y=3x^3/2 on 1≤x≤3
3) The force on a particle is described by 5x^3+5 at a point xx
along the x-axis. Find the work done in moving the particle from
the origin to x=8
4) Find the work done for a force F =12/x^2 N from x =2 to x =3
m.
5) A force of 77 pounds is required to hold a spring stretched
0.1 feet beyond...

For the questions below, consider the following function.
f (x) = 3x^4 - 8x^3 + 6x^2
(a) Find the critical point(s) of f.
(b) Determine the intervals on which f is increasing or
decreasing.
(c) Determine the intervals on which f is concave up or concave
down.
(d) Determine whether each critical point is a local maximum, a
local minimum, or neither.

Use the method of Lagrange Multipliers to find the extreme
value(s) of f(x, y) = 3x + 2y subject to the constraint y = 3x ^2 .
Identify the extremum/extrema as maximum or minimum.

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