Eric Nicholas K's answer to Elle's Junior College 2 H2 Maths Singapore question.
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I might be wrong because the workings are too short for a 7 mark question.
Date Posted:
3 years ago
Elle : for c, as long as c < 0, you will always have two stationary points for this question.
y = ½x³ + cx
dy/dx = 3/2 x² + c
When dy/dx = 0, 3/2 x² + c = 0
x² = -2c/3
x² has to be positive in order to have two real roots (x² < 0 means imaginary/complex roots will be obtained, x² = 0 means only 1 real root of 0)
So for -2c/3 > 0, c < 0
As for the mark allocation,
4m → getting the general solution
3m → getting a particular solution and sketching the curve.
Not too little at all.
y = ½x³ + cx
dy/dx = 3/2 x² + c
When dy/dx = 0, 3/2 x² + c = 0
x² = -2c/3
x² has to be positive in order to have two real roots (x² < 0 means imaginary/complex roots will be obtained, x² = 0 means only 1 real root of 0)
So for -2c/3 > 0, c < 0
As for the mark allocation,
4m → getting the general solution
3m → getting a particular solution and sketching the curve.
Not too little at all.
thankss
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