Question

5. Find the open intervals on which f(x) =x^3−6x^2−36x+ 2 is increasing, as well as the open intervals on which f(x) is decreasing.

- How do you know when the function is increasing or decreasing? Please show all work.

6. Find the open interval on which f(x) =x^3−6x^2−36x+ 2 has upward concavity, as well as the open intervals on which f(x) has downward con-cavity.

- How do you know if a function has an upward concavity or downward concavity? Please show all work.

7. Find all x-values at which local extrema of f(x) =x^3−6x^2−36x+ 2 occur. Indicate whether each extremum is a maximum or a minimum.

- How do you know if the value you have is a minimum or maxiumu? Please show all work.

8. Sketch the graph of f(x) =x3−6x2−36x+ 2. Your graph does not need to be precise, but it should have the correct basic shape based on your answer to Problems 5-7

Please show all work.

Answer #1

consider the function f(x) = x/1-x^2
(a) Find the open intervals on which f is increasing or
decreasing. Determine any local minimum and maximum values of the
function. Hint: f'(x) = x^2+1/(x^2-1)^2.
(b) Find the open intervals on which the graph of f is concave
upward or concave downward. Determine any inflection points. Hint
f''(x) = -(2x(x^2+3))/(x^2-1)^3.

Let f(x)=6x^2−2x^4. Find the open intervals on which f is
increasing (decreasing). Then determine the x-coordinates of all
relative maxima (minima).
1.
f is increasing on the intervals
2.
f is decreasing on the intervals
3.
The relative maxima of f occur at x =
4.
The relative minima of f occur at x =

find the open intervals where f(x) = x √ 4 − x 2 is increasing
or decreasing algebraically
find the open intervals where f(x) = −x 3 + 4x 2 − 6 is concave
upward or concave downward algebraically
the
radical goes overvthe whoe equation over 4-x^2

If f(x)-x^3-3x;
a) find the intervals on which f is increasing or
decreasing.
b)find the local maximum and minimum values
c)find the intervals of concavity and inflection points
d)use the information above to sketch and graph of f

- Suppose f is a function such that f′(x) = (x+ 1)(x−2)2(x−3),
so that f has the critical points x=−1,2,3. Determine the open
intervals on which f is increasing/decreasing.
- Let f be the same function as in Problem 9. Determine which,
if any, of the critical points is the location of a local extremum,
and indicate whether each extremum is a maximum or minimum.
Im confused on how to figure out if a function is increasing and
decreasing and...

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

Find the intervals on which f is increasing or decreasing. Find
the local maximum and minimum values of f. Find the intervals of
concavity and the inflection points. f(x) = x √ 6 − x

Find the open intervals on which f(x)=x^4 + 8x^3 is increasing
or decreasing.

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

For the function f(x)=−3x^3+36x+6
(a) Find all intervals where the function is
increasing.
Answer: ff is increasing on=
(b) Find all intervals where the function is
decreasing.
Answer: ff is decreasing on=
(c) Find all critical points of f(x)
Answer: critical points: x=
Instructions:
For parts (a) and (b), give your
answer as an interval or a union of intervals, such as
(-infinity,8] or (1,5) U
(7,10) .
For part (c), enter your xx-values as a
comma-separated list, or none...

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