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February 20th, 2019, 10:16 PM   #1
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Exclamation Concavity and Second Derivative Test Problems Help

Can you help on these sets of problems?
I don't understand entirely how to do them, and I have a test coming soon, so I could really use your help. Thanks.

2.$\ \ \ $Suppose you are given a formula for a function $f$.

a)$\ \ \ $How do you determine where $f$ is increasing or decreasing?

b)$\ \ \ $How do you determine where the graph of $f$ is concave upward or downward?

c)$\ \ \ $How do you locate inflection points?

4.$\ \ \ $If $f(x) = \frac{x^2}{x^2 - 1}$, find (a) the intervals on which $f$ is increasing or decreasing, (b) the $x$-values of local maximum and minimum values, and (c) the intervals of concavity and inflection points. Justify each response.

6.$\ \ \ $If $f(x) = x + \frac4x$, find all relative extrema using the second derivative test. Justify your response.

Last edited by skipjack; February 21st, 2019 at 06:31 AM.
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February 21st, 2019, 06:44 AM   #2
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What is implied if the derivative of the function exists and is positive throughout an interval?
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