Question

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.

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

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...

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

Let f(x)=4+12x−x^3. Find (a) the intervals on which ff is
increasing, (b) the intervals on which ff is decreasing, (c) the
open intervals on which ff is concave up, (d) the open intervals on
which f is concave down, and (e) the x-coordinates of all
inflection points.
(a) f is increasing on the interval(s) =
(b) f is decreasing on the interval(s) =
(c) f is concave up on the open interval(s) =
(d) f is concave down on the...

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)

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 curve f(x) = 2x 3 − 9x 2 + 12x − 5, find (i) the local
maximum and minimum values, (ii), the intervals on which f is
increasing or decreasing, and (iii) the intervals of concavity and
the inflection points.

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: _________________

Find the intervals on which the graph of f is concave upward,
the intervals on which the graph of f is concave downward, and the
x, y coordinates of the inflection points. Circle your final
answers.
6). f(x) = -x^3 – 3x^2 + 5x – 4
7). f(x) = 3x^4 – 18x^2

1, Let f be a function such that f′′(x) =x(x+ 1)(x−2)^2. Find
the open intervals on which is concave up/down.
2. An inflection point is an x-value at which the concavity of a
function changes. For example, if f is concave up to the left of
x=c and f is concave down to the right of x=c, then x=c is an
inflection point. Find all inflection points in the function from
Problem 1.

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