Question

given function f(x)=-x^3+5x^2-3x+2

A) Determine the intervals where F(x) Is increasing and
decreasing

b) use your answer from a to determine any relative maxima or
minima of the function

c) Find that intervals where f(x) is concave up and concave
down and any points of inflection

Answer #1

Analyze and sketch the graph of the function f(x) = (x −
4)2/3
(a) Determine the intervals on which f(x) is increasing /
decreasing
(b) Determine if any critical values correspond to a relative
maxima / minima
(c) Find possible inflection points
(d) Determine intervals where f(x) is concave up / down

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

Given the function g(x) = x3-3x + 1, use the first and second
derivative tests to
(a) Find the intervals where g(x) is increasing and
decreasing.
(b) Find the points where the function reaches all realtive
maxima and minima.
(c) Determine the intervals for which g(x) is concave up and
concave down.
(d) Determine all points of inflection for g(x).
(e) Graph g(x). Label your axes, extrema, and point(s) of
inflection.

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)...

what does a derivative tell us?
F(x)=2x^2-5x-3, [-3,-1]
F(x)=x^2+2x-1, [0,1]
Give the intervals where the function is increasing or
decreasing?
Identify the local maxima and minima
Identify concavity and 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 ?(?) = ?^3 + 3x^2 + 1 determine
All intervals where the graph is concave up
All intervals where the graph is concave down
The coordinates of any points of inflection

1.f(x)= e-2^(x)
a. Give in interval notation the intervals where is increasing
and where is decreasing.
b. Give in interval notation the intervals where is concave up
and where is concave down.
c. Give the coordinates of any points of inflection.
d. Sketch the curve

Find the intervals where f(x) = 2x3 + 3x2
- 36x + 7 is increasing, decreasing, concave up, concave down, and
the inflection points.

Consider the graph y=x^3+3x^2-24x+10
Determine:
a) interval(s) on which it is increasing
b) interval(s) on which it is decreasing
c) any local maxima or minima
d) interval(s) on which it is concave up
e) interval(s) on which it is concave down
f) any point(s) of inflection

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