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.

Printable View

- May 10th 2012, 10:56 AMsarahheath1985Find any stationary points of this function.
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. - May 10th 2012, 11:51 AMtom@ballooncalculusRe: Find any stationary points of this function.
Just in case a picture helps with the quotient rule...

http://www.ballooncalculus.org/draw/diffProd/nine.png

... 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.

__________________________________________________ __________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - May 10th 2012, 01:01 PMsarahheath1985Re: Find any stationary points of this function.
Hi,

Thanks. I can see where I was going wrong now.

How would you apply this to the first derivative test though?

Cheers - May 10th 2012, 01:50 PMtom@ballooncalculusRe: Find any stationary points of this function.
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.