Curve Analysis Question please help!

Question

How do I draw a graph that satisfies the following criteria?

f''(x) >0 when x<1 and x>3

f''(x) <0 when 1<x<3

f'(1) =0 and f'(6) =0

no x-intercepts

Answer 1

if there's no x intercepts, that eliminates cubic equations, and half standard up & downward opening parabolas and eliminates all right or left opening parabolas

No linear equations can fit the change in slope, with changing 2nd derivatives

It looks like a sine or cosine curve shifted up or down so there are no x intercepts

possibly a cosx curve shifted to the right by pi/5 and up by more than 1 or down by more than 1

with domain limited to 0<x<6

maybe

f(x)= cos(x-pi/5) + 2

just a standard cosine curve with the same period, shifted to the right and up