1. ## Proofs

a) Show that, if f is convex, then -f is concave (and vice versa)

b) Show that the following function, having domain {0,1,...,n-1}, is convex:
f(j) = 1 / (n-j)

I know what convex/concave looks like, but not sure what it means in a formula. Any help would be great thanks!

2. Originally Posted by jaclyn91
a) Show that, if f is convex, then -f is concave (and vice versa)

b) Show that the following function, having domain {0,1,...,n-1}, is convex:
f(j) = 1 / (n-j)

I know what convex/concave looks like, but not sure what it means in a formula. Any help would be great thanks!
convex means $\forall x,y,\lambda\in [0,1],f(\lambda x+(1-\lambda)y)\leq\lambda f(x)+(1-\lambda)f(y)$
or $\forall x
or $f'(x)$exists and it is non-decreasing
or $f''(x)\geq 0$
for concave, you just replace all > with <!