Stationary points: the first-derivative sign test

Year 12 Mathematics Advanced · drag x along the curve · f′ decides the classification, f gives the y-value
Function

f above, f′ below

f(x) f′(x) stationary
Drag the cursor across each stationary point and watch the sign of f′ either side of it.
−3

Arrow keys move the cursor by 0.05.

f(x) 0
f′(x) 0
sign of f′ ?
0

C shifts f up or down. Watch what it does to f′ and to the table.

f′(x) = s · (x − p)m (x − q). You choose the roots and the multiplicity; f is the antiderivative with f(0) = 0.

−1
2

Sign table

Cells fill in as the cursor visits each interval. Predict each stationary point before you scrub past it.