AP Calc AB Unit 5

Critical Point

when f’(x)=0 or undefined

Relative max

when f’ changes from positive to negative

Relative min

when f’ changes from negative to positive

f’’(x)>0

function concave up

f’’(x)<0

function concave down

f’’>0

f’ is increasing

f’’<0

f’ is decreasing

Point of Inflection

f’’(x) changes signs (f’’=0)

f’(x)=0 and f’’(x)>0

relative minimum

f’(x)=0 and f’’(x)<0

relative max

f’(x)=0 and f’’(x)=0

inconclusive