Question

Which functions fit the description?

function 1: f(x)=x^2 + 12. function 2: f(x)= −e^x^2 - 1. function 3: f(x)= e^3x function 4: f(x)=x^5 -2x^3 -1

a. this function defined over all realnumbers has 3 inflection points

b. this function has no global minimum on the interval (0,1)

c. this function defined over all real numbers has a global min but no global max

d. this function defined over all real numbers is non-decreasing everywhere

e. this function (defined over all real numbers) has no critical points or inflection points

Answer #1

The function f(x) = 3x 4 − 4x 3 + 12 is defined for all real
numbers. Where is the function f(x) decreasing?
(a) (1,∞) (b) (−∞, 1) (c) (0, 1) (d) Everywhere (e) Nowhere

4. Given the function y = f(x) = 2x^3 + 3x^2 – 12x +
2
a. Find the intervals where f is increasing/f is
decreasing
b. Find the intervals where f is concave up/f is concave
down
c. Find all relative max and relative min (state which
is which and why)
d. Find all inflection points (also state
why)

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

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.

6. Let ?(?) be a continuous function defined for all real
numbers, with?'(?)=(?−1)2(?−3)3(?−2)
and
?''(?) = (? − 1)(3? − 7)(2? − 3)(? − 3)2.
On what intervals is ? increasing and decreasing?
Increasing on:
Decreasing on:
Find the x-coordinate(s) of all local minima and maxima of
?.
Local min at x=__________________
Local max at x=_________________
c. On what intervals if ? concave up and concave down?
Concave up on:
Concave down on:
d. Find the x-coordinate(s) of points of...

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?

Given the function
h(x)=e^-x^2
Find first derivative f ‘ and second derivative
f''
Find the critical Numbers and determine the intervals
where h(x) is increasing and decreasing.
Find the point of inflection (if it exists) and determine
the intervals where h(x) concaves up and concaves
down.
Find the local Max/Min (including the
y-coordinate)

- Suppose f is a function such that f′(x) = (x+ 1)(x−2)2(x−3),
so that f has the critical points x=−1,2,3. Determine the open
intervals on which f is increasing/decreasing.
- Let f be the same function as in Problem 9. Determine which,
if any, of the critical points is the location of a local extremum,
and indicate whether each extremum is a maximum or minimum.
Im confused on how to figure out if a function is increasing and
decreasing and...

consider the function f(x) = x/1-x^2
(a) Find the open intervals on which f is increasing or
decreasing. Determine any local minimum and maximum values of the
function. Hint: f'(x) = x^2+1/(x^2-1)^2.
(b) Find the open intervals on which the graph of f is concave
upward or concave downward. Determine any inflection points. Hint
f''(x) = -(2x(x^2+3))/(x^2-1)^3.

For f(x)=2+3x+x3 find:
A.increasing and decreasing intervals
B. Local max and min coordinates
C. Concativity Intervals (UP & DOWN INTERVALS)
D. Inflection points coordinates
E. Graph of f(x)

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