Question

Absolute Maxima and Minima:

1. Use the methods discussed in Ch 3.4 to find the absolute maximum
and minimum values of ?, if any,

on the given interval, and state where those values occur. Show all your work in order to receive full credit. (14pts)

?(?) = 4?^4/3 − 3?^1/3; [−1, 8)

Answer #1

Find the absolute maximum and minimum values of f(x)=
−x^3−3x^2+4x+3, if any, over the interval
(−∞,+∞)(−∞,+∞).
I know it doesn't have absolute maxima and minima but where do
they occur? In other words x= ? for the maxima and minima?

1. find the absolute maxima and minima for f (x) on the interval
[a, b].
f(x)=9+6x2-x3 [-3,10]

Find the absolute maximum and minimum values of the following
function on the given interval. If there are multiple points in a
single category list the points in increasing order in x value and
enter N in any blank that you don't need to use. f(x)=3(x2−1)3,
[−1,2]
Absolute maxima
x = y =
x = y =
x= y =
Absolute minima
x = y =
x = y =
x = y =

Find the absolute maximum and minimum values of the following
function over the given interval. If there are multiple points in a
single category list the points in increasing order in x value and
enter N in any blank that you don't need to use.
f(x)=(4cosx)/(14+7sinx), 0≤x≤2π
Absolute maxima
x = y =
x = y =
x = y =
Absolute minima
x = y =
x = y =
x = y =

Question 1. Find the first few maxima and minima for the
diffraction pattern of two slits separated by 12 μm with a screen
50 cm away assuming we use a laser with a wavelength in air of 550
nm.
Question 2. Using these values sketch a graph of light intensity
versus distance from the central maximum (y = 0).
Question 3. If you then examine two slits separated by 1.2 μm
what wavelength light should you use to keep the...

Use the first derivative test to find the relative maxima and
minima of the function f (x) = 3x^4 + 8x^3 – 90x^2 + 1,200 on the
domain (–∞, 7]. Determine the intervals of
increase and decrease on this domain. Complete the answer box, if
there are no answers, write “NONE.” SHOW WORK.
Crit Points:
Intervals of increase:
Intervals of decrease:
Coords of relative max
Coords of relative min

3 parts use these answers/rules
Find the relative extrema of the function Specifically:
The relative maxima of f occur at x =
The relative minima of f occur at x =
The value of f at its relative minimum is
the value of f at its relative maximum is
Notes: Your answer should be a comma-separated list of values or
the word "none".
part 1)
f(x)=x^2+6x+5
part 2)
f(x)= x^3-18x+5
part 3)
f(x)=8x^4−4x^2+8

Find the local maxima and minima values for the function f(x)=
e^(x^5-x^4-2x^3+x^2-1)

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 ?

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]

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