Question

**Find the following and graph for
f(x)=16x(x-1)^3**

f '(x)=

f ''(x)=

C.V.=

increasing:

decreasing;

Point of inflection:

Concave up and down:

Domain

Local max and min:

Answer #1

1. For the function y=x^1/3(x+4), find
a. Find where the function is increasing and decreasing
b. Local max and mins
c. Intervals of concave up and concave down
d. Points of inflection.
Include y-values

How do I graph a function with the following properties?
increasing: (-∞, 1)
decreasing: (1, 3), (3, ∞)
local max: (1, 8)
intercepts: (0,0), (3, 0)
concave down: (-∞, 2), (3, ∞)
concave up: (2, 3)
inflection points: (2, 5), (3, 0)

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.

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) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

Let f(x) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

1. The critical point(s) of the function
2. The interval(s) of increasing and decreasing
3. The local extrema
4. The interval(s) of concave up and concave down
5. The inflection point(s).
f(x) = (x^2 − 2x + 2)e^x

Let
f(x)=(x^2)/(x-2) Find the following
a) Domain of f
b) Intercepts (approximate to the nearest thousandth)
c) Symmetry (Show testing for symmetry)
d) asymptotes
e) Intervals of increase/decrease (approximate the critical
numbers to the nearest thousandth. Be sure to show the values
tested)
f) Local maxima and local minima
g) Intervals of concavity and points of inflection (be sure to
show all testing)
h) summary for f(x)=(x^2)/(x-2)
Domain
X intercepts:
Y intercept:
symmetry:
asymptote:
increasing:
decreasing:
local max:
local min:...

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?

f(x)=2x ln x
find what intervals on the graph of the function are increasing
and decreasing and identify local max and min points

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