Question

2. The function f(x) = 1 1 + 1.25x 2 has one inflection point on the interval 0 ≤ x ≤ 2.

(a) Find the inflection point of the function f(x). Write the answer with ALL the decimal places the calculator gives. Do not round the calculator answer. calculator answer:

(b)Sketch the graph of f(x) over the interval 0 ≤ x ≤ 2. Label the inflection point of f(x) in your sketch. Give the window you use.

(c)(2 points) Use the graph to decide what kind of inflection point g(x) has. Circle one of the following.

(A) Point of fastest decrease (B) Point of slowest decrease (C) Point of fastest increase (D) Point of slowest increase

Answer #1

Consider the function f(x)=arctan((x+5)/(x+4))
What is the slope of the tangent line at the inflection point? The
inflection point I got was: (-9/2, -pi/4).
If you could provide a sketch of the graph as well I'll give a
thumbs up, thank you!

question number 1:
Find the point of inflection of the graph of the function. (If
an answer does not exist, enter DNE.)
f(x) = x + 7 cos x, [0, 2π]
(x, y)
=
DNE
(smaller x-value)
(x, y)
=
DNE
(larger x-value)
Describe the concavity. (Enter your answers using interval
notation. If an answer does not exist, enter DNE.)
concave upward
DNE
concave downward
question number 2:
Find the points of inflection of the graph of the...

the function f(x) = ex - 2e-2x - 3/2 is
graphed at right. evidently, f(x) has a zero in the interval
(0,1).
(a) show that f(x) is increasing on (-infinity, infinity) (so
that no other zero of f exists.)
(b) use one iteration of Newton's method to estimate the zero,
starting with initial estimate x1 = 0.
(c) it appears from the graph that f(x) has an inflection point
at or near the zero of f. find the exact coordinates...

1. Consider the function ??(??)=2??^3?12??^2+50
a. Use calculus to find the inflection point.
b. Identify all intervals where the function is concave up.
*Hint: Use calculator window [?5,10] × [?50,150].

Consider the function f(x) = −x3 + 4x2 + 7x + 1.
(a) Use the first and second derivative tests to determine the
intervals of increase and decrease, the
local maxima and minima, the intervals of concavity, and the
points of inflection.
(b) Use your work in part (a) to compute a suitable table of
x-values and corresponding y-values and carefully sketch the graph
of the function f(x). In your graph, make sure to indicate any
local extrema and any...

1. You are given the function f(x) = x/(1−x)
a) Find the x and y- intercepts.
b) Find the horizontal asymptote(s).
c) Find the vertical asymptote(s) and do a limit analysis of the
behavior of f on either
side of each vertical asymptote.
d) Find the critical number(s) of f.
e) Find the interval(s) of increase and decrease of f.
f) Find the relative maximum and minimum value(s) of f.
g) Find the hypercritical number(s) of f.
h) Find the...

(1 point) Consider the function f(x)=x^2 e^6x
f(x) has two inflection values at x = C and x = D with C≤D
where C is
and D is
Finally for each of the following intervals, tell whether f(x) is
concave up (type in CU) or concave down (type in CD).
(−∞,C]:
[C,D]:
[D,∞):

Consider the function below. (If an answer does not exist, enter
DNE.)
f(x) = 1/2x^(4) − 4x^(2) + 3
(a)
Find the interval of increase. (Enter your answer using interval
notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b)
Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c)
Find the inflection points.
(x, y) = (smaller x-value)
(x, y) =...

Which of the following is true about the graph of
f(x)=8x^2+(2/x)−4?
a) f(x) is increasing on the interval
(−∞,0).
b) f(x) has a vertical asymptote at
x=2.
c) f(x) is concave down on the interval
(0,∞).
d) f(x) has a point of inflection at the point
(0,−4).
e) f(x) has a local minimum at the point
(0.50,2).
Suppose
f(x)=12xe^(−2x^2)
Find any inflection points.

For the function y = x 3 − 2x 2 − 1, use the first and second
derivative tests to
(a) determine the intervals of increase and decrease.
(b) determine the local (relative) maxima and minima.
(c) determine the intervals of concavity.
(d) determine the points of inflection.
(e) sketch the graph with the above information indicated on the
graph.

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