O-LevelAdditional MathematicsLogarithmic and exponential functions4037/11 · Oct/Nov 2010 · Q1211 Marks
OR A curve has the equation `y = Ae^(2x) + Be⁻ˣ` where `x ≥ 0`. At the point where `x = 0`, `y = 50` and `dy/dx = -20`.
- (i)Show that `A = 10` and find the value of B.[5]
- (ii)Using the values of A and B found in part (i), find the coordinates of the stationary point on the curve.[4]
- (iii)Determine the nature of the stationary point, giving a reason for your answer.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- B1
- M1 M1 for attempt to differentiate
- A1 A1 all correct
- DM1 DM1 for attempt to solve equations.
- A1
- M1 M1 for equating to zero and attempt at solution
- M1 M1 for dealing with exponentials
- M1 M1 for attempt to obtain x
- A1 A1 for both
- M1 M1 for attempt at second derivative or other valid method
- A1 A1 for a correct conclusion
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