Lorenzo went to the store with 20$. He bought some cans of soup for 2$ each and a gallon of milk for 3$. He had 1$ left over.
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There are three things you have to know:
- A function is convex when its second derivative
- A function is concave when it second derivative
- The derivative of a power,
, is
So, the first derivative is
and the second derivative is
This implies that the second derivative of a parabola is constant, and of course that 2 doesn't change the sign of .