Question

4. Let ℎ(?) = ln(3? 2 + 1). a. (10 pts.) Find the intervals of concavity. SHOW WORK!!!

b. (4 pts.) Find any inflection points.

Answer #1

Let f(x)=2x^3 - 9x^2 +12x -4
Find the intervals of which f is increasing or decreasing
Find the local maximum and minimum values of f
Find the intervals of concavity and the inflection points

let
f(x) = x^4 -4x+10, Find the intervals of increase and decrease.
for the same function find relative extrema as ordered
pairs.
for the same function find intervals of concavity (concave
up/down) and any inflection points as ordered pairs.

Let
f(x)=((x+1)^2)/((x−1)^2)
(a) (8 pts) Find the intervals on which
f
increases and the intervals on which f decreases. Find
all the local maximum and minimum values of f
.
(b) Find the intervals on which f
is concave upward and concave downward. Find the inflection
points.

1. Let ?(?)=−?4−4?3+8?−1. Find the open intervals on which ? is
concave up (down). Then determine the ?-coordinates of all
inflection points of ?.
2. Find the x-values of all inflection points for the graph
?(?)=2?4+18?3−30?2+15f(x)=2x4+18x3−30x2+15. (Give your answers as a
comma separated list, e.g., 3,-2.)
3. Let f(x)=1/4x2+7. Find the open intervals on which ?f is
concave up (down). Then determine the ?x-coordinates of all
inflection points of ?.
4. Let ?(?)=6?−3/?+4 Find the open intervals on which ?f...

List any extrema, inflection point, intervals of concavity, and
then sketch the graph.
?(?)=?3 −?2 −?+1

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.

Let f (x) = −x^4− 4x^3. (i) Find the intervals of
increase/decrease of f . (ii) Find the local extrema of f (values
and locations). (iii) Determine the intervals of concavity. (iv)
Find the location of the inflection points of f. (v) Sketch the
graph of f

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

4. Let ?(?) = ?? ? − ?? ? .
a) Find the intervals on which the graph of ? is concave upward
and the intervals over which the graph of ? is concave
downward.
Concave Up: ___________________________ Concave Down:
_____________________________
b) State the coordinates of any inflection points on the graph
of ?.
Coordinates: _________________

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]

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