A-LevelMathematicsDifferentiation9709/31 · May/June 2020 · Q46 Marks
The curve with equation y = e^(2x)(sin x + 3 cos x) has a stationary point in the interval 0 ≤ x ≤ π.
- (a)Find the x-coordinate of this point, giving your answer correct to 2 decimal places.[4]
- (b)Determine whether the stationary point is a maximum or a minimum.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] (a) Use product rule
- [A1] (a) Obtain derivative in any correct form e.g. 2e^(2x)(sin x + 3 cos x) + e^(2x)(cos x − 3 sin x)
- [M1] (a) Equate derivative to zero and obtain an equation in one trigonometric ratio
- [A1] (a) Obtain x = 1.43 only
- [M1] (b) Use a correct method to determine the nature of the stationary point e.g. x = 1.42, y' = 0.06e^(2.84) > 0; x = 1.44, y' = −0.07e^(2.88) < 0
- [A1] (b) Show that it is a maximum point
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