Question

Prove, using the second derivative, that the general quadratic y= ax^2+bx+c, is:
a) always convex when a>0
b) always concave when a <0

Answer 1

Answer:

dy/dx = 2ax + b

d²y/dx² = 2a

2a < 0

When a < 0

(So concave)

2a > 0

When a > 0

(So convex)