Question

Givenf(x)=x3−6x2+15

(a) Find the critical numbers of f.

(b) Find the open intervals on which the function is increasing or decreasing.

(c) Apply the First Derivative Test to identify all relative extrema (that is, all relative minimums and maximums).

Answer #1

Find all critical numbers, the open intervals on which f(x) is
increasing or decreasing, and locate and classify all relative
extrema.
f (x) = x3- 13/2
x2- 10x + 7
and
f (x)= x1/3 (x-4)

f(x)= x^4-2x^2-3. Using the first derivative test, find:
a. All critical Numbers
b. Intervals on which f(x) is increasing or decreasing
c. location and value of all relative extrema

For f(x) = 2x4 - 4x2 + 1 find the open
intervals in which the function is increasing and decreasing.
Find open intervals where the function is concave up and concave
down.
Sketch the graph of the function - label all local maximums, all
local minimums, and any inflection points.

Given the function f(x) = x3 - 3x2 - 9x + 10
Find the intervals where it is increasing and
decreasing and find the co-ordinates of the relative maximums &
minimums.
Find the intervals where it is concave up and down and
co-ordinates of any inflection points
Graph the f(x)

For the function below, find (a) the critical numbers; (b)
the open intervals where the function is increasing; and (c) the
open intervals where it is decreasing. f(x)=x+7/x+1

Given f(x)= x3 -
6x2-15x+30
Determine f ’(x)
Define “critical point” of a function. Then determine the
critical points of f(x).
Use the sign of f ’(x) to determine the interval(s) on which
the function is increasing and the interval(s) on which it is
decreasing.
Use the results from (c) to determine the location and values
(x and y-values of the relative maxima and the relative minima of
f(x).
Determine f ’’(x)
On which intervals is the graph of f(x)...

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 4. (A) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) (B) Apply the First Derivative Test to identify all
relative extrema.

Use Calculus to find the open intervals on [0, 2pi) for which
the function f(x) = cos x - sin2 x is increasing or
decreasing. Identify any local extrema, specifying the coordinates
of each point.

Use Calculus to find the open intervals on [0, 2PI ) for which
the function f(x) = cosx - sinx is increasing or decreasing.
Identify any local extrema, specifying the coordinates of each
point.

f(x)=5x^(2/3)-2x^(5/3)
a. Give the domain of f
b. Find the critical numbers of f
c. Create a number line to determine the intervals on which f is
increasing and decreasing.
d. Use the First Derivative Test to determine whether each
critical point corresponds to a relative maximum, minimum, or
neither.

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