Curve Sketching (1 Viewer)

[goobi]

So this is a table that I've made for transforming the graph of f(x) into that of f'(x) or vice versa. Can anyone please read over it and fill out the blanks for me? Thanks

f(x)	f'(x)
Positive tangents	Above x-axis
Negative tangents	Below x-axis
Concaving up	??
Concaving down	??
Stationary points	Zeroes
Horizontal points of inflexion	Zeroes
Vertical points of inflexion	??
??	Stationary points
??	Horizontal points of inflexion
??	Vertical points of inflexion

<tbody>
</tbody>

 

[4025808]

When f'(x) has stationary points, f(x) is an inflexion point, from what i know.