What is the difference between a stationary point and a turning point?

• A?stationary point?is a point at which the?gradient function?is equal to zero
  • The?tangent?to the?curve?of the?function?is?horizontal
• A?turning point?exhibits this property, but in addition the?function changes?from?increasing?to?decreasing,?or?vice versa
  • The curve?‘turns’?from?‘going upwards’?to?‘going downwards’?or?vice versa
  • Turning points?will either be?(local) minimum?or?maximum?points
• A?point?of?inflection?could?also be a?stationary point?but is?not?a turning point

How do I find stationary points and turning points?

What are local minimum and maximum points?

similar for a global?maximum point

How do I find the nature of a stationary point?

• The?nature?of a?stationary point?can be determined using the?first derivative?but it is?usually?quicker and easier to use the?second derivative
  • only in cases when the second derivative is?zero?is the first derivative method needed