Suppose that212f(x)(A) Find all critical values of f, compute their average, and enter it below.Note: If there are no critical values, enter -1000Average of critical values =(B) Use interval notation to indicate where f(x) is increasing.Note: Enter T' for, '-I' for -, and 'U' for the union symbol.If you have extra boxes, fill each in with an 'x'Increasing:(C) Use interval notation to indicate where f(x) is decreasingDecreasing:(D) Find the x-coordinates of all local maxima of f, compute their average, and enter it below.Note: If there are no local maxima, enter -1000Average of x values =(E) Find the x-coordinates of all local minima of f, compute their average, and enter it belowNote: If there are no local minima, enter -1000.Average of x values =(F) Use interval notation to indicate where f(x) is concave up.Concave up:(G) Use interval notation to indicate where f(x) is concave down.Concave down(H) Find all inflection points off, compute their average, and enter it belowNote: If there are no inflection points, enter -1000Average of inflection points =(I) Find all horizontal asymptotes of f, compute the average of the y values, and enter it belowNote: If there are no horizontal asymptotes, enter -1000Average of horizontal asymptotes = |(J) Find all vertical asymptotes off, compute the average of the x values, and enter it belowNote: If there are no vertical asymptotes, enter -1000Average of vertical asymptotes = |(K) Use all of the preceding information to sketch a graph off. When you're finished, enter a "1" in the box below.Graph Complete:

Question
Asked Nov 28, 2019
19 views

Section G,H,I

Suppose that
212
f(x)
(A) Find all critical values of f, compute their average, and enter it below.
Note: If there are no critical values, enter -1000
Average of critical values =
(B) Use interval notation to indicate where f(x) is increasing.
Note: Enter T' for, '-I' for -, and 'U' for the union symbol.
If you have extra boxes, fill each in with an 'x'
Increasing:
(C) Use interval notation to indicate where f(x) is decreasing
Decreasing:
(D) Find the x-coordinates of all local maxima of f, compute their average, and enter it below.
Note: If there are no local maxima, enter -1000
Average of x values =
(E) Find the x-coordinates of all local minima of f, compute their average, and enter it below
Note: If there are no local minima, enter -1000.
Average of x values =
(F) Use interval notation to indicate where f(x) is concave up.
Concave up:
(G) Use interval notation to indicate where f(x) is concave down.
Concave down
(H) Find all inflection points off, compute their average, and enter it below
Note: If there are no inflection points, enter -1000
Average of inflection points =
(I) Find all horizontal asymptotes of f, compute the average of the y values, and enter it below
Note: If there are no horizontal asymptotes, enter -1000
Average of horizontal asymptotes = |
(J) Find all vertical asymptotes off, compute the average of the x values, and enter it below
Note: If there are no vertical asymptotes, enter -1000
Average of vertical asymptotes = |
(K) Use all of the preceding information to sketch a graph off. When you're finished, enter a "1" in the box below.
Graph Complete:
help_outline

Image Transcriptionclose

Suppose that 212 f(x) (A) Find all critical values of f, compute their average, and enter it below. Note: If there are no critical values, enter -1000 Average of critical values = (B) Use interval notation to indicate where f(x) is increasing. Note: Enter T' for, '-I' for -, and 'U' for the union symbol. If you have extra boxes, fill each in with an 'x' Increasing: (C) Use interval notation to indicate where f(x) is decreasing Decreasing: (D) Find the x-coordinates of all local maxima of f, compute their average, and enter it below. Note: If there are no local maxima, enter -1000 Average of x values = (E) Find the x-coordinates of all local minima of f, compute their average, and enter it below Note: If there are no local minima, enter -1000. Average of x values = (F) Use interval notation to indicate where f(x) is concave up. Concave up: (G) Use interval notation to indicate where f(x) is concave down. Concave down (H) Find all inflection points off, compute their average, and enter it below Note: If there are no inflection points, enter -1000 Average of inflection points = (I) Find all horizontal asymptotes of f, compute the average of the y values, and enter it below Note: If there are no horizontal asymptotes, enter -1000 Average of horizontal asymptotes = | (J) Find all vertical asymptotes off, compute the average of the x values, and enter it below Note: If there are no vertical asymptotes, enter -1000 Average of vertical asymptotes = | (K) Use all of the preceding information to sketch a graph off. When you're finished, enter a "1" in the box below. Graph Complete:

fullscreen
check_circle

Expert Answer

Step 1

Part (G):

Concave downward interval:

If F’’(x) <0, the function is concave down.

help_outline

Image Transcriptionclose

Given 2r2 f (x) x2+4 Step 1: Find second derivative off Differentiate fw.r.tx f(xd 2x2 d =2- +4 +4 Using Quotient rule (2t) (a2-n4)-2}(2) f(x)2 2 16x f'(x) (2-4 x°+4

fullscreen
Step 2

Now, differentiate f w.r.t x,

help_outline

Image Transcriptionclose

Apply Quotient rue 1x4 4x +4 f"(x) 16 2 +4 16-3x24 f"(x) 3 +4

fullscreen
Step 3

Substitute f"...

help_outline

Image Transcriptionclose

16-3x2+4 3 (s2 4 0=16-3x24 3x2=4 4 3 2 3 Rationalize the denominator 2/3 x=t 3

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Functions