Point of inflection confusion

[brazen plume]

Hi everyone! my question is shouldn't the graph exist NONE point of inflections? since the graph of f' never reaches negative so it never changes direction on a graph therefore the f(x) graph should be the one i drew in red right?

[severe narwhal]

Attention: A point of inflection occurs when the slope of f'(x) changes signs.

That is, when f'(x) changes directions from down to up or vice versa.

You can think of a point of inflection of a function as the point at which the function changes curvature.

[brazen plume]

Ohh but was the graph I drew of f(x) correct though? A straight slope up graph?

[severe narwhal]

That can't be right considering that f'(x) is negative for x<0 and zero for x=3.

[brazen plume]

Ohh okay

I understand I think I was just traditionally used to seeing point of inflections as a

That shape

Thank you!!

.solved

[rancid loom]

Solved

Post marked as solved by @brazen plume.

Use .unsolved if this was a mistake.