f(x) = 3 sinx+ 3 cosx

0 ≤x≤ 2πHow do I use this to find local max & min, critical points, and inflection points?

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- Nov 1st 2010, 06:06 PMlooseenz2Graphing using 1st and 2nd derivatives
*f*(*x*) = 3 sin*x*+ 3 cos*x*

0 ≤*x*≤ 2*π*How do I use this to find local max & min, critical points, and inflection points?

- Nov 2nd 2010, 02:52 AMUnknown008
I'm not sure of what you have to do, but if you have to graph f(x), you can convert it into a simple form:

The first and second derivative should also be easier to graph now, provided you know how to graph f(x). - Nov 2nd 2010, 04:08 AMHallsofIvy
"Critical points" are, by definition, points where the first derivative is 0. "Local max and min" are points where the first derivative changes sign (and so the second derivative is not 0), and inflection points are where the second derivative is 0.

f'(x)= 3cos(x)- 3 sin(x)

That will equal 0 when cos(x)- sin(x)= 0 or cos(x)= sin(x). That happens when or .

f''(x)= -3 sin(x)- 3cos(x)

That will equal 0 when sin(x)+ cos(x)= 0 or cos(x)=-sin(x). That happens when or .

( , not .) - Nov 2nd 2010, 04:20 AMUnknown008
Oops... dang (Doh)