Let f(A)=(det(A))1/n. And assume domain of f is space of positive semi definite symmetric n x n matrices with real entries. Show that f is concave: f((1−t)A+tB))>=(1−t)f(A)+tf(B) for t in [0,1].

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function
$f(x,y)=x^3-6xy+8y^3$

$\frac{1}{\sec <!--\; \; -->(x)}$ in derivative?

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