The Second Derivative
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The second derivative is what you get when you differentiate the derivative.

Stationary Points
The second derivative can be used as an easier way of determining the nature of stationary points.

A stationary point on a curve occurs when dy/dx = 0. Once you have established where there is a stationary point, the type of stationary point (maximum, minimum or point of inflexion) can be determined using the second derivative.

If d²y  is positive, then it is a minimum point.
  dx²
If d²y is negative, then it is a maximum point.
  dx²
If d²y is zero, then it could be a max, a min or a point of inflexion.
  dx²
If d²y/dx² = 0, you must test the values of dy/dx either side of the stationary point, as before.

© Matthew Pinkey

Other Notes in this Category

1. Chain, Product and Quotient
2. Differential Equations
3. Differentiation
4. Differentiation from 1st Principles
5. Differentiation of Trig Funcns
6. Exponentials & Logarithms
7. Implicit Differentiation
8. Integration
9. Integration by Parts
10. Integration by Substitution
11. Tangents and Normals
12. The Second Derivative
13. Uses of Differentiation
14. Volumes of Revolution

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