Difference between revisions of "009A Sample Final 2, Problem 10"

Revision as of 19:30, 17 February 2017

Let

f(x)={\frac {4x}{x^{2}+1}}

a) Find all local maximum and local minimum values of

f,

find all intervals where

f

is increasing and all intervals where

f

is decreasing.

b) Find all inflection points of the function

f,

find all intervals where the function

f

is concave upward and all intervals where

f

is concave downward.

c) Find all horizontal asymptotes of the graph

y=f(x).

d) Sketch the graph of

y=f(x).

Solution:

(a)

Step 2:

(b)

Step 1:

Step 2:

(c)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam">Let
+::<math>f(x)=\frac{4x}{x^2+1}</math>
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::<span class="exam">a) Find all local maximum and local minimum values of <math>f,</math> find all intervals where <math>f</math> is increasing and all intervals where <math>f</math> is decreasing.
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+::<span class="exam">b) Find all inflection points of the function <math>f,</math> find all intervals where the function <math>f</math> is concave upward and all intervals where <math>f</math> is concave downward.
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
+::<span class="exam">c) Find all horizontal asymptotes of the graph <math>y=f(x).</math>
+::<span class="exam">d) Sketch the graph of <math>y=f(x).</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"