IB DP Maths: AA HL复习笔记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
转载自savemyexams
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