Question

**Given the function and the bounded
interval,**

**f x( )= x3 −6x2 − 45x+ 4 [-5,10]**

**F. The interval where the function is concave down is
_______.**

**G. The interval where the function is concave up is
__________.**

**H. The global maximum value in the bounded interval [-5,
10] is __________. (y coordinate).**

**I. The global minimum value in the bounded interval [-5,
10] is ___________. (y coordinate).**

**Show your work please.**

Answer #1

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Given f(x)= x3 -
6x2-15x+30
Determine f ’(x)
Define “critical point” of a function. Then determine the
critical points of f(x).
Use the sign of f ’(x) to determine the interval(s) on which
the function is increasing and the interval(s) on which it is
decreasing.
Use the results from (c) to determine the location and values
(x and y-values of the relative maxima and the relative minima of
f(x).
Determine f ’’(x)
On which intervals is the graph of f(x)...

Consider the following. f(x) = 4x3 − 6x2 − 24x + 4
(a) Find the intervals on which f is increasing or decreasing.
(Enter your answers using interval notation.) increasing
decreasing
(b) Find the local maximum and minimum values of f. (If an
answer does not exist, enter DNE.) local minimum value local
maximum value
(c) Find the intervals of concavity and the inflection points.
(Enter your answers using interval notation.)
concave up concave down inflection point (x, y) =

1. (Continued) Consider the function
(e)
(f)
f (x) = x3 − 7 x + 5. 2
(0.5 pt) Find the possible inflection points of f(x). Show
work.
(0.5 pt) Test the possible inflection points of f(x) to
determine if each point is or is not an inflection point. Your work
must show that you tested each point properly and support your
conclusion. Be sure to state your conclusion. Show work.
(g)
(1 pt) Find the global minimum and global...

Consider the function x3−6x2+9x+3.8. Find the global maximum of
the function on the interval [2,3.3]. Round your answer to two
decimal places.

1.) Suppose g(x) = x2− 3x.
On the interval [0, 4], use calculus to identify x-coordinate of
each local / global minimum / maximum value of g(x).
2.) For the function f(x) = x 4 − x 3 + 7...
a.) Show that the critical points are at x = 0 and x = 3/4 (Plug
these into the derivative, what you get should tell you that they
are critical points).
b.) Identify all intervals where f(x) is increasing
c.)...

a) If g(x) = x3−6x2 −15x + 7, ﬁnd the interval(s) on which g is
increasing/decreasing, and identify the location(s) of any local
max/mins. Make a sign chart for g'
b) Suppose f(x) =(x2 −3)/(x2 + 3) [Note that x2 + 3
> 0 for all x.] Using the fact that f''(x) = −36(x2 −1)/(x2 +
3)3 ﬁnd the interval(s) on which f is concave up/concave down, and
identify the location(s) of any inﬂection points. Make a sign chart
for f''

Compute the integral of the function
f(x) = -x3 + 6x2 + 1
in the interval 0 to 3 using
A. Simpson’s 1/3 rule using two intervals
AND
B. Simpson’s 3/8 rule using two intervals

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)

f(x)=x3-6x2+9x+2 on interval [2,4]
Find any local and absolute extreme values of the function on
the given interval.

Problem 43.)
a.) Use Excel to graph the function f(x) = x3 -6x2 + 9x -6 for
-2 ≤ x ≤ 5. (OK to draw the graph neatly on your homework, or cut
and paste from Excel.)
b.) Does it look the graph has both a relative maximum point
and relative minimum point? Estimate them from the graph.
c.) Find the points where the derivative f ’(x) = 0 and
compare to your answers from (b.)

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