Convexity when First Derivative is a Constant

Question

I was trying to get the convexity of f(x) = x but then the first derivative was just a constant one and if I get the second derivative it would just give me a zero, does this mean that it's both concave and convex?

score 2 · Answer 1 · answered Jul 17 '19 at 07:25

2

Yes, any linear function $f(x)=ax+b$ is both concave and convex. And these are the only functions with this property.

answered Jul 17 '19 at 07:25

Kavi Rama Murthy

311,013

score 2 · Answer 2 · answered Jul 17 '19 at 07:29

2

Yes, it is both concave and convex. You don't need derivatives for this. Just use the definitions of concave function and of convex function.

answered Jul 17 '19 at 07:29

José Carlos Santos

427,504

Convexity when First Derivative is a Constant

2 Answers2