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junior college 2 | H2 Maths
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Hello! I would really appreciate if someone could help me with part (iii)! Thank you in advance!
Date Posted: 4 years ago
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2x2 - 3xy + y2 = 5
Differentiating with respect to x,
4x - 3 [x dy/dx + y] + 2y dy/dx = 0
4x - 3x dy/dx - 3y + 2y dy/dx = 0
[2y - 3x] dy/dx = 3y - 4x
dy/dx = (3y - 4x) / (2y - 3x)
Suppose dy/dx = 0 (ie tangent is parallel to the horizontal x axis).
3y - 4x = 0
y = 4x/3
Substituting this to the original equation,
2x2 - 3x (4x/3) + (4x/3)^2 = 5
2x2 - 4x2 + 16x2/9 = 5
-2x2/9 = 5
Then,
x2 = -45/2
with no real roots and therefore there exists no point in the curve in which the tangent is parallel to the x axis.
Differentiating with respect to x,
4x - 3 [x dy/dx + y] + 2y dy/dx = 0
4x - 3x dy/dx - 3y + 2y dy/dx = 0
[2y - 3x] dy/dx = 3y - 4x
dy/dx = (3y - 4x) / (2y - 3x)
Suppose dy/dx = 0 (ie tangent is parallel to the horizontal x axis).
3y - 4x = 0
y = 4x/3
Substituting this to the original equation,
2x2 - 3x (4x/3) + (4x/3)^2 = 5
2x2 - 4x2 + 16x2/9 = 5
-2x2/9 = 5
Then,
x2 = -45/2
with no real roots and therefore there exists no point in the curve in which the tangent is parallel to the x axis.
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