Question

what does a derivative tell us?

F(x)=2x^2-5x-3, [-3,-1]

F(x)=x^2+2x-1, [0,1]

Give the intervals where the function is increasing or decreasing?

Identify the local maxima and minima

Identify concavity and inflection points

Answer #1

given function f(x)=-x^3+5x^2-3x+2
A) Determine the intervals where F(x) Is increasing and
decreasing
b) use your answer from a to determine any relative maxima or
minima of the function
c) Find that intervals where f(x) is concave up and concave
down and any points of inflection

For the function f(x)=x^3+5x^2-8x , determine the intervals
where the function is increasing and decreasing and also find any
relative maxima and/or minima. Increasing ____________________
Decreasing ___________________ Relative Maxima _______________
Relative Minima _______________

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.

consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?

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

Consider the function
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

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.

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)=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 =

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