Determine if following functions are convex, concave, quasiconvex or quasiconcave? Explain please

Question

1. y=x²

2. y=arctanx

3. y=e^x

4.y=3x+2

5.y=-x⁴

6. y=x-sinx

Answer 1

 

 

1. y=x2   concave
2. y=arctanx    quasiconcave
3. y=ex     concave
4.y=3x+2    quasiconcave
5.y=-x4      convex
6. y=x-sinx     quasiconcave