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

Revision as of 19:02, 18 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"> Let
-::::<math>f(x)=4+8x^3-x^4</math>
+::<math>f(x)=4+8x^3-x^4</math>
-::<span class="exam">a) Over what <math>x</math>-intervals is <math>f</math> increasing/decreasing?
+<span class="exam">(a) Over what <math>x</math>-intervals is <math>f</math> increasing/decreasing?
-::<span class="exam">b) Find all critical points of <math>f</math> and test each for local maximum and local minimum.
+<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">(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>
+<span class="exam">(d) Sketch the shape of the graph of <math>f.</math>
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 |}
 '''Solution:'''
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 |}
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