- #1
22990atinesh
- 143
- 1
I understand the 1st derivative test for testing concavity which says
The graph of a differentiable function y=f(x) is
1. concave up on an interval I if f' is increasing on I.
2. concave down on an interval I if f' is decreasing on I.
But I'm confused with 2nd derivative test which says
Let y=f(x) is twice differentiable on an interval I
1. If f'' > 0 on I, the graph of f over I is concave up.
2. If f'' < 0 on I, the graph of f over I is concave down.
If f'' < 0 or f'' > 0, then it means its a number (negative or positive). Which means f' is linear and function quadratic. Please correct me If I'm wrong.