Question

3. Given the function ?(?) = (x^3/3)-(3x^2/2)+2x:

a. Find all critical numbers.

b. Identify which, if any, critical numbers are local max or min and explain your answer.

c. Find any inflection points and give the x value.

d. On the interval [0.6, 2.6] identify the absolute max and min, if any. and justify your answer.

e. Give the interval where the curve is concave up and justify your answer.

Answer #1

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)

6. Let ?(?) be a continuous function defined for all real
numbers, with?'(?)=(?−1)2(?−3)3(?−2)
and
?''(?) = (? − 1)(3? − 7)(2? − 3)(? − 3)2.
On what intervals is ? increasing and decreasing?
Increasing on:
Decreasing on:
Find the x-coordinate(s) of all local minima and maxima of
?.
Local min at x=__________________
Local max at x=_________________
c. On what intervals if ? concave up and concave down?
Concave up on:
Concave down on:
d. Find the x-coordinate(s) of points of...

Given a function?(?)= −?5 +5?−10, −2 ≤ ? ≤ 2
(a) Find critical numbers
(b) Find the increasing interval and decreasing interval of
f
(c) Find the local minimum and local maximum values of f
(d) Find the global minimum and global maximum values of f
(e) Find the inflection points
(f) Find the interval on which f is concave up and concave
down
(g) Sketch for function based on the information from part
(a)-(f)

Suppose that
f(x)=x−3x^1/3
(A) Find all critical values of f. If there are no critical values,
enter -1000. If there are more than one, enter them separated by
commas.
Critical value(s) =
(B) Use interval notation to indicate where f(x) is
increasing.
Note: When using interval notation in WeBWorK,
you use INF for ∞∞, -INF for
−∞−∞, and U for the union symbol. If there are no
values that satisfy the required condition, then enter "{}" without
the quotation marks....

consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?

Find the intervals on which f(x) = x^4 + 2x^3 − 36x^2 + 9x − 47
is concave down and up, along with the x-coordinates of any
inflection points. Justify all your work.

For full credit be sure to show all work and units.
1. A 20 foot ladder leans against a vertical wall. The bottom of
the ladder slides away from the wall at 2 ft/sec.
a. How fast is the top of the ladder sliding down the wall when
the top of the ladder is 12 feet from the ground?
b. Interpret the meaning of the sign.
2. The current speed record for weight loss is 487 pounds to 130
pounds...

.Given: f '(x) = x^2 (x-1) (x-2),
a) Find three first order critical values of f(x).
b) Categorize what is happening at each of them (e.g. rel max,
rel min, etc).
c) What is the degree of f(x)?
d) How many infiection points does f(x) have?
2.) Find the absolute max. value of f(x) =2x^3+ 3x^2 - 12x- 1on
the closed interval [0,2]

For the following function, find where they are
increasing/decre
asing, concave up/down and
any critical numbers and inflection points.
f(x) = x^2+ 3x – 5

find the graph g(x) x^4+2x^3+1; (1)fint the intervals on which
g(x) is increasing or decreasing (2)find local max and min (3)find
the intervals of concavity and the inflection points.

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