IB DP Maths: AA HL復(fù)習(xí)筆記5.2.4 Further Applications of Differentiation
Stationary Points & Turning Points
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?
Testing for Local Minimum & Maximum 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
Exam Tip
- Exam questions may use the phrase “classify turning points” instead of “find the nature of turning points”
- Using your GDC to sketch the curve is a valid test for the nature of a stationary point in an exam unless the question says "show that..." or asks for an algebraic method
- Even if required to show a full algebraic solution you can still use your GDC to tell you what you’re aiming for and to check your work
Worked Example
轉(zhuǎn)載自savemyexams
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