Critical Points

Critical Pointsundefined isor 0 occur when points Critical

dxdy

Critical Pointsundefined isor 0 occur when points Critical

dxdy

y

x

Critical Pointsundefined isor 0 occur when points Critical

dxdy

y

x

Critical Pointsundefined isor 0 occur when points Critical

dxdy

y

x

point turningmaximum ,0 xf

Critical Pointsundefined isor 0 occur when points Critical

dxdy

y

x

point turningmaximum ,0 xf

point turningminimum ,0 xf

y

x

y

x

y

x

inflection ofpoint horizontal ,0 xf

y

x

y

x

inflection ofpoint horizontal ,0 xf

y

x

y

x

inflection ofpoint horizontal ,0 xf

tangent vertical,undefined is xf

y

x

y

x

y

x

point minimum

continuousnot is curve cusp"" ,undefined is xf

y

x

point minimum

continuousnot is curve cusp"" ,undefined is xf

Exercise 10C; 1, 2ace etc, 3, 5, 8, 10