Graphs 9
3 marks · NormalExplain how you can use the second derivative to classify stationary points of a cubic function.
Illustrate your answer by referring to the function .
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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A stationary point is a maximum if and a minimum if . For , the stationary points are at and ; at , (maximum), at , (minimum).
Common mistakes: Not stating which sign is max/min; Using only first derivative
Show mark scheme and worked solution
Marking points
B1 · 1 mark · States the test: is maximum, is minimum.
M1 · 1 mark · Applies to a cubic, finds stationary points.
A1 · 1 mark · Correctly classifies at least one stationary point using second derivative.
Worked solution
To classify a stationary point of a cubic, differentiate once to find , set to zero to find stationary points.
At x=0: d^2y/dx^2 = -6 (max), x=2: d^2y/dx^2=6 (min).