Find any stationary points of this function and state whether they are local max or min.
g(x)=(e^(-3x+2sinx)/6)/(3+2cosx) 0<x<2pi included.
Just in case a picture helps with the quotient rule...
... where (key in spoiler) ...
Spoiler:
Ignore the denominator, and the exponential which can't be zero. So you have...
$\displaystyle 4 \cos^2 x - 9 + 2 \sin x = 0$
Apply pythagoras.
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
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Do you mean the second? Setting the first derivative to zero as we've just done to find the stationary points is the first. (Apply Pythag and solve the quadratic.)
Finding the +/- sign of the second derivative at these points determines whether the curve is, following it left to right, headed ultimately up (because turning out of a minimum) or down (coming out of a maximum). (The 'second derivative test'.)
But determining whether min or max is often (probably here) easier just by testing the values of the original function around the stationary point.