Question

the global maximum of the function h(x)=1/x^2 + 1 defined on (-infinity, infinity) is: a) 1 b) 0 c) 1/2 d) DNE

Consider a family of functions f(x)=e^-ax + e^ax for a does not = 0. which of the following holds for every member of the family?

a) f is always increasing b) f is always concave up c) f has no critical points

Answer #1

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...

(A). Find the maximum of the following utility function with
respect to x;
U= x^2 * (120-4x).
The utility function is U(x,y)= sqrt(x) + sqrt(y) . The price of
good x is Px and the price of good y is Py. We denote income by M
with M > 0. This function is well-defined for x>0 and
y>0.
(B). Compute (aU/aX) and (a^2u/ax^2). Is the utility function
increasing in x? Is the utility function concave in x?
(C). Write down...

1. At x = 1, the function g( x ) = 5x ln(x) −
3x
is . . .
Group of answer choices
has a critical point and is concave up
decreasing and concave up
decreasing and concave down
increasing and concave up
increasing and concave down
2. The maximum value of the function f ( x ) = 5xe^−2x
over the domain [ 0 , 2 ] is y = …
Group of answer choices
10/e
0
5/2e
e^2/5...

the function g(x) is increasing on (-infinity, 2) and (5,
infinity). The function is decreasing on (2,4) and (4,5). The
function is concave down on (-infinity, 3) and (4,5) and (5,
infinity). The function is concave up on (3,4). Give a sketch of
the curve. (you do not need precise y-values. You need the correct
shape of the curve)

Given a function?(?)= −?5 +5?−10, −2 ≤ ? ≤ 2
(a) Find critical numbers
(b) Find the increasing interval and decreasing interval of
f
(c) Find the local minimum and local maximum values of f
(d) Find the global minimum and global maximum values of f
(e) Find the inflection points
(f) Find the interval on which f is concave up and concave
down
(g) Sketch for function based on the information from part
(a)-(f)

1.) Suppose g(x) = x2− 3x.
On the interval [0, 4], use calculus to identify x-coordinate of
each local / global minimum / maximum value of g(x).
2.) For the function f(x) = x 4 − x 3 + 7...
a.) Show that the critical points are at x = 0 and x = 3/4 (Plug
these into the derivative, what you get should tell you that they
are critical points).
b.) Identify all intervals where f(x) is increasing
c.)...

Find the global maximum and global minimum of the function f(x)
= √( 1 − x^ 2) on [−1, 1/2].

a) The function f(x)=ax^2+8x+b, where a and b are
constants, has a local maximum at the point (2,15). Find the values
of a and b.
b) if b is a positive constand and x> 0, find the
critical points of the function g(x)= x-b ln x, and determine if
this critical point is a local maximum using the second derivative
test.

The continuous function has exactly one critical point. Find the
x-values at which the global maximum and the global minimum occur
in the interval given.
a) f'(1) = 0, f"(1) = -2 on 1 ≤ x ≤ 3
b) g'(-5) = 0, g"(-5) = 2 on -6 ≤ x ≤ -5

find the interval where the function is increasing and
decreasing f(x) =(x-8)^2/3
a) decreasing (8, infinity) increasing (-infinity, 8) local max
f(8)=0
a) decreasing (- infinity, 8) increasing (8, infinity) local max
f(8)=0
a) decreasing (-infinity, infinity) no extrema
a) increasing (-infinity, infinitely) no extrema

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