Do convex/concave curves have a negative/positive gradient?

[jon80]

We are studying indifference curves in economics, and these are applied to marginal utility calculations, thus some mathematical background would be appreciated. Do convex curves have a negative or positive dy/dx? Would you kindly explain the theorem please?

[stapel_eliz]

To relate concavity to derivatives, you'll need to look at the Second Derivative Test.