It turns out that your friends have allergies to chicken and now they're into moto-cross. They have a small square backyard which is 4m long and 4m wide. They want to create a hill area so that they can have moto-cross fun in the backyard. More precisely, they want that there are four nicely spaced-out hills! The following functions comes to your mind :

f(x,y) = 10x^2y^2e^(?x^2?y^2) + 20

Explain to your friend how the plot of this function could help them to model their backyard! Specifically, do the following: determine all stationary points of f (x, y) and classify those for which the Hessian test is not inconclusive; explain what this has to do with your friend's design for the backyard.

Note: For the classification of stationary points, you are not required to compute the Hessian matrix by hand, but you can simply use WolframAlpha to compute the required determinant values; you need to write down these values and explain what they tell you!

It turns out that your friends have allergies to chicken and now they're into moto-cross. They have a small square backyard which is 4m long and 4m wide. They want to create a hill area so that they can have moto-cross fun in the backyard. More precisely, they want that there are four nicely spaced-out hills! You remember your lectures and the following functions comes to your mind (of course!): f(x, y) = 10x2y e 2-y" + 20. Explain to your friend how the plot of this function could help them to model their backyard! Specifically, do the following: determine all stationary points of f (x, y) and classify those for which the Hessian test is not inconclusive; explain what this has to do with your friend's design for the backyard. Note: For the classification of stationary points, you are not required to compute the Hessian matrix by hand, but you can simply use WolframAlpha to compute the required determinant values; you need to write down these values and explain what they tell you