Question

Determine the critical numbers?

f(x) = x^3 + 5/2x^2 - 28x

Answer #1

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.

find critical numbers of
f(x)=2x^3 + x^2 - 2x
please show all work :)

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

1- For the following functions, find all critical numbers
exactly.
f(x) = x − 2 sin x for −2π < x < 2π
f(x) = e^−x −e^−3x for x > 0
f(x) = x^5 − 2x^3

Verify the quotient rule for each of the following:
1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2
2. f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1

Find the critical point of the function g(x)=ln(x^(2)+2x+3).
Then determine whether the critical point is a local minimum or
local maximum.

let
y= -x^3 + 6x^2 - 5
a. find all critical numbers for f(x).
b. find the absolute extrema on the interval (-1,3).
c. find the absolute extrema on the interval (1,3).

3. Given the function ?(?) = (x^3/3)-(3x^2/2)+2x:
a. Find all critical numbers.
b. Identify which, if any, critical numbers are local max or min
and explain your answer.
c. Find any inflection points and give the x value.
d. On the interval [0.6, 2.6] identify the absolute max and min,
if any. and justify your answer.
e. Give the interval where the curve is concave up and justify
your answer.

F(x) = ( (x+3)/(x+1) )2
find the domain of F
and any critical numbers, horizontal asymptotes, vertical
asymptotes and points of inflection

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.

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