1. ### Generalized Fourier Integral and Steepest descent path, Saddle point near the endpoin

I am looking forward to solving the integration in the following equation with the assumption that $ka$ is very large \begin{align} H = 2jka\int_{-\pi/2}^{\pi/2}\cos{(\varphi-\phi)}e^{jka[\cos{\varphi}+\cos{(\varphi-\phi)}]}\ d\varphi \end{align} I used the steepest descent path method to...
2. ### Find relative extrema and saddle points

Given f(x,y) = x^3 + 3xy + y^3 + 4, find all relative extrema and saddle points... can someone help me? I don't know how to do this problem. I can get fx and fy, but I don't know from there.
3. ### Local max, local min, or saddle point

I have a function g(x,y) = x^2*y - x - 1 for which my partial derivatives set equal to 0 are 2xy - 1 = 0 and x^2 = 0. Solving the 2nd equation, I get x = 0. If I plug in 0 into the first equation, both x and y goes away because they are being multiplied by 0. What to do in this case ? I have to...