Posted by Bob on Thursday, January 8, 2009 at 7:36pm.
Let f be the function given by
f(x)=2ln(x^2+3)x with domain 3 is less than or equal to x which is less than or equal to 5
a) Find the xcoordinate of each relative maximum point and each relative minimum point of f. Justify your answer.
b) Find the xcoordinate of each inflection point of f.
c) Find the absolute maximum value of
f(x).

Calc  Reiny, Thursday, January 8, 2009 at 9:13pm
f'(x) = 2(2x)/(x^2 + 1)  1
= 0 for max/min
for this I got x = 2 ± √5
These lie within your domain so
You will have to find
f(3), f(2+√5)), f(2√5) and f(5) to see which is the maximum
for f''(x) I got (4(x^2 + 1)  4x(2x))/(x^2 + 2)^2
setting this equal to zero, I got x = ± √2
sub back in the original to find the two inflection points.
f(3)
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