Question

1. What is a relative min extrema (x,y) for f(x) in f(x) =
2x^{3}+3x^{2}-12x+5 ?

2. Use a number line and test points to show where f(x) in f(x)
= -2x^{3}-1/2 x^{2}+x-3 is concave up and down

3. use a number line and test points to show where f(x) in
2x^{3}+3x^{2}-36x+20 is increasing and
decreasing

Answer #1

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

Suppose f(x) = 2x3 + 3x2 - 12x + 1.
a)
- find the domain,
- intervals of increase/decrease (on number line),
- intervals of concavity (on number line),
- turning points (on number line)
- and inflection points (on number line)
b)
Sketch the graph of 2x3 + 3x2 - 12x + 1
and clearly label turning points, inflection points, and the
y-intercept
Please share your step by step neatly
Thank you so much!

4. Given the function y = f(x) = 2x^3 + 3x^2 – 12x +
2
a. Find the intervals where f is increasing/f is
decreasing
b. Find the intervals where f is concave up/f is concave
down
c. Find all relative max and relative min (state which
is which and why)
d. Find all inflection points (also state
why)

Identify the absolute and relative maximum and minimum of
f (x) = 2x3 –
3x2 – 36x + 40
on [-3, 4]

Let f (x) = 2x3 + 3x2 −12x + 6.
(1) Find the intervals of increase or decrease.
(2) Find the local maximum and minimum values.
(3) Find the intervals of concavity and the inflection points.
(d) Use the information from parts (a)-(c) to sketch the graph

For the function f(x)=x^5+5x^4-4. Write "none" if there isn't an
answer.
(a) find all local extrema of this function, if any, and
increasing and decreasing intervals.
Local max:___ Local min:___ Increasing:___ Decreasing:___
(b) Find all the inflection points of this function, if ay. And
concave up and concave down intervals.
Inflection points:___ concave up:___ concave down:___
(c) Use part a and b to sketch the graph of the function. Must
label important points and show proper concavity.

f(x)= 12x- x^3
1. where is the local min? x-value
2. where is fhe local max? x-value
3. what is the inflection point? (x and y)
4. for which interval is the graph "concave down"?
for
what interval is the graph concave up?

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]

Consider the equation below.
f(x) =
2x3 + 3x2
− 72x
(a) Find the interval on which f is increasing. (Enter
your answer in interval notation.)
Find the interval on which f is decreasing. (Enter your
answer in interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum
local maximum
(c) Find the inflection point.
(x, y) =
Find the interval on which f is concave up. (Enter your
answer in interval notation.)
Find the...

For the function
f(x) =x(x−4)^3
•
Find all
x-intercepts and find the
y-intercept
•
Find all critical numbers,
•
Determine where the function is increasing and where it is
decreasing,
•
Find and classify the relative extrema,
•
Determine where the function is concave up and where it is
concave down,
•
Find any inflection points, and Use this information to sketch
the graph of the function.
•
Use this information to sketch the graph of the function.

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