Difference between revisions of "009A Sample Final 3, Problem 6"

Revision as of 19:34, 17 February 2017

Let

f(x)=4+8x^{3}-x^{4}

a) Over what

x

-intervals is

f

increasing/decreasing?

b) Find all critical points of

f

and test each for local maximum and local minimum.

c) Over what

x

-intervals is

f

concave up/down?

d) Sketch the shape of the graph of

f.

Solution:

(a)

Step 2:

(b)

Step 1:

Step 2:

(c)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam"> Let
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::::<math>f(x)=4+8x^3-x^4</math>
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+::<span class="exam">a) Over what <math>x</math>-intervals is <math>f</math> increasing/decreasing?
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
+::<span class="exam">b) Find all critical points of <math>f</math> and test each for local maximum and local minimum.
+::<span class="exam">c) Over what <math>x</math>-intervals is <math>f</math> concave up/down?
+::<span class="exam">d) Sketch the shape of the graph of <math>f.</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"