Difference between revisions of "009A Sample Final 1, Problem 9"

Revision as of 21:26, 1 February 2016

Given the function $f(x)=x^{3}-6x^{2}+5$ ,

a) Find the intervals in which the function increases or decreases.

b) Find the local maximum and local minimum values.

c) Find the intervals in which the function concaves upward or concaves downward.

d) Find the inflection point(s).

e) Use the above information (a) to (d) to sketch the graph of

y=f(x)

.

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

(c)

Step 1:

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+<span class="exam">Given the function <math>f(x)=x^3-6x^2+5</math>,
+::<span class="exam">a) Find the intervals in which the function increases or decreases.
+::<span class="exam">b) Find the local maximum and local minimum values.
+::<span class="exam">c) Find the intervals in which the function concaves upward or concaves downward.
+::<span class="exam">d) Find the inflection point(s).
+::<span class="exam">e) Use the above information (a) to (d) to sketch the graph of <math>y=f(x)</math>.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;