Question

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)

Answer #1

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1. For the function y=x^1/3(x+4), find
a. Find where the function is increasing and decreasing
b. Local max and mins
c. Intervals of concave up and concave down
d. Points of inflection.
Include y-values

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

1.f(x)= e-2^(x)
a. Give in interval notation the intervals where is increasing
and where is decreasing.
b. Give in interval notation the intervals where is concave up
and where is concave down.
c. Give the coordinates of any points of inflection.
d. Sketch the curve

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...

7. Sketch complete graphs of the following; indicate where the
function is increasing/decreasing, has local extrema, where the
graph is concave up or concave down, asymptotes and coordinate
intercepts
(a) ?(?)=(1/5)?5−? (b) ?(?)=(3?+2)/?

1. The critical point(s) of the function
2. The interval(s) of increasing and decreasing
3. The local extrema
4. The interval(s) of concave up and concave down
5. The inflection point(s).
f(x) = (x^2 − 2x + 2)e^x

Given the following function: Y= (2x + 1)3 (x-1)
a) Determine where the function is increasing or decreasing. b)
Determine where the function is concave up or down

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

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)

For the function
f(x) =x(x−4)^3
•
Find all
x-intercepts and find the
y-intercept
•
Find all critical numbers,
•
Determine where the function is increasing and where it is
decreasing,
•
Find and classify the relative extrema,
•
Determine where the function is concave up and where it is
concave down,
•
Find any inflection points, and Use this information to sketch
the graph of the function.
•
Use this information to sketch the graph of the function.

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