Problems

01

Study of critical points

Find the critical points of the following functions, and analyze them using the discriminant test (or state that the test fails). You may use a calculator or computer to evaluate the discriminant at the critical points.

• (a) $f(x,y)=x^3+y^3-3x^2-3y^2-9x$
• (b) $f(x,y)=\left(6x-x^2\right)\left(4y-y^2\right)$
• (c) $f(x,y)=x-y^2-\ln \left(x+y\right).$