Edexcel IALMathematicsGeneral Applications9 Marks
The curve C has equation y = 2x + cot x, 0 < x < π.
- (a)Find dy/dx.[2]
- (b)Find the range of values for x for which y is increasing.[7]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- (a) M1 for differentiating 2x to 2 and cot x to -csc² x.
- (a) A1 for dy/dx = 2 - csc² x.
- (b) M1 for setting their dy/dx > 0.
- (b) A1 for 2 - csc² x > 0 ⇒ csc² x < 2 ⇒ sin² x > 1/2.
- (b) M1 for sin x > 1/√2 or sin x < -1/√2 (or equivalent inequality with sin x).
- (b) A1 for critical values x = π/4 and x = 3π/4.
- (b) M1 for considering the range 0 < x < π.
- (b) A1 for correctly identifying the interval π/4 < x < 3π/4.
- (b) A1 for final answer in terms of x, with correct strict inequalities.
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