A-LevelMathematicsDifferentiation9709/32 · May/June 2021 · Q88 Marks
The equation of a curve is y = e⁻⁵ˣ tan²x for −π/2 < x < π/2. Find the x-coordinates of the stationary points of the curve. Give your answers correct to 3 decimal places where appropriate.
- The equation of a curve is y = e⁻⁵ˣ tan²x for −π/2 < x < π/2. Find the x-coordinates of the stationary points of the curve. Give your answers correct to 3 decimal places where appropriate.[8]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] Use correct product (or quotient) rule
- [A1] Obtain dy/dx = −5e⁻⁵ˣ tan²x + 2e⁻⁵ˣ tan x sec²x
- [M1] Equate their derivative to zero, use sec²x = 1+tan²x and obtain an equation in tan x
- [A1] Obtain 2 tan²x−5 tan x+2=0
- [B1] State answer x = 0
- [M1] Solve a 3 term quadratic in tan x and obtain a value of x
- [A1] Obtain answer, e.g. 0.464
- [A1] Obtain second non-zero answer, e.g. 1.107 and no other in the given interval
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