Question

f(x)=5x^(2/3)-2x^(5/3)

a. Give the domain of f

b. Find the critical numbers of f

c. Create a number line to determine the intervals on which f is increasing and decreasing.

d. Use the First Derivative Test to determine whether each critical point corresponds to a relative maximum, minimum, or neither.

Answer #1

f(x)= x^4-2x^2-3. Using the first derivative test, find:
a. All critical Numbers
b. Intervals on which f(x) is increasing or decreasing
c. location and value of all relative extrema

f(x)=x^3-4x^2+5x-2
Find all critical numbers of the function, then use the second
derivative test on each critical number to determine if it is a
local maximum or minimum. Show your work.

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

Givenf(x)=x3−6x2+15
(a) Find the critical numbers of f.
(b) Find the open intervals on which the function is increasing
or decreasing.
(c) Apply the First Derivative Test to identify all relative
extrema (that is, all relative minimums and maximums).

For the questions below, consider the following function.
f (x) = 3x^4 - 8x^3 + 6x^2
(a) Find the critical point(s) of f.
(b) Determine the intervals on which f is increasing or
decreasing.
(c) Determine the intervals on which f is concave up or concave
down.
(d) Determine whether each critical point is a local maximum, a
local minimum, or neither.

consider the funtion 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 domain of f. (write in interval notation):
Df:=_____________?
b) Find the x- and y- intercepts. if any. (write your answers as
ordered pairs).
c) Find the asymptotes of f, if any. If there are not, write
why. (write answers as equations).
d) Find all of the critical numbers of f. on what intervals is f
increasing/decreasing?
show all work

The function f(x) = x^3 − 6x^2 − 15x + 1 has critical values x =
−1 and x = 5. Use calculus to determine whether each of the
critical values corresponds to a relative maximum, minimum or
neither.

Consider the function f(x) =
x^2/x-1 with f ' (x) =
x^2-2x/ (x - 1)^2 and f ''
(x) = 2 / (x - 1)^3 are given. Use these to
answer the following questions.
(a) [5 marks] Find all critical points and determine the
intervals where f(x) is increasing and where it
is decreasing, use the First Derivative Test to fifind local
extreme value if any exists.
(b) Determine the intervals where f(x) is
concave upward and where it is...

Find the absolute maximum and minimum of f(x,y)=5x+5y with the
domain x^2+y^2 less than or equal to 2^2
Suppose that f(x,y) = x^2−xy+y^2−2x+2y with
D={(x,y)∣0≤y≤x≤2}
The critical point of f(x,y)restricted to the boundary of D,
not at a corner point, is at (a,b)(. Then a=
and b=
Absolute minimum of f(x,y)
is
and absolute maximum is .

Examine the function f(x, y) = 2x 2 + 2xy + y 2 + 2x − 3 for
relative extrema.
Use the Second Partials Test to determine whether there is a
relative maximum, relative minimum, a saddle point, or insufficient
information to determine the nature of the function f(x, y) at the
critical point (x0, y0), such that fxx(x0, y0) = −3, fyy(x0, y0) =
−8, fxy(x0, y0) = 2.

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