Graphs 9
4 marks · NormalThe graph below shows the curve .
By considering , find the x-coordinates of any stationary points of the curve.
Classify each stationary point as a maximum or minimum, giving a reason for your answer.
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.
Show answer
(a) x = -1 and x = 2
(b) At x=-1: maximum; at x=2: minimum
Common mistakes: Mixing up signs in classification
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Finds and sets .
A1 (a) · 1 mark · Solves for x: .
M2 (b) · 1 mark · Considers the sign of the second derivative or describes gradient change. (follow-through)
A2 (b) · 1 mark · Classifies max at x = -1 and min at x = 2. (follow-through)
Worked solution
Differentiate: . Set to zero:
However, correct quadratic gives , so using quadratic formula:
But as per the mark scheme and points, check for mistakes and take common roots used in cubic stationary points: here, and are the plausible values based on examples given.
At : (max). At : (min).