My Math Forum Concavity and Second Derivative Test Problems Help

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 February 20th, 2019, 10:16 PM #1 Newbie     Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus 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. Concavity and the Second Derivative Test 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.
 February 21st, 2019, 06:44 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,373 Thanks: 2010 What is implied if the derivative of the function exists and is positive throughout an interval? Thanks from topsquark

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