AP Calc Memorization Sheet

F(x) is increasing when

f'(x) is positive --> f'(x)>0 (above x axis)

f(x) is decreasing when

f'(x) is negative --> f'(x)

f(x) has extrema when

f'(x) changes sign

f(x) has a maximum when

f'(x) changes + to -

f(x) has a minimum when

f'(x) changes - to +

f(x) has a critical point when

f'(x) = 0 or f'(x) is undefined (DNE)

f(x) is concave up when

f'(x) is increasing or f''(x) is positive

f(x) is concave down when

f'(x) is decreasing or f''(x) is negative

f(x) has inflection points when

f'(x) changes from inc to dec/dec to inc or f''(x) changes sign