Suppose f:R^n->R is twice differentiable. Prove that f is convex if and only if its Hessian gradiant^2 f(x) is nonnegative.

Not sure how to approach this beside the fact that i'll have to prove in both directions since it's if and only if.

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- February 24th 2008, 08:50 PMjenny01convex due to nonnegative hessian proof
Suppose f:R^n->R is twice differentiable. Prove that f is convex if and only if its Hessian gradiant^2 f(x) is nonnegative.

Not sure how to approach this beside the fact that i'll have to prove in both directions since it's if and only if.