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Question
Find the tangent and normal to the following curves at the given points on the curve
y = x2 – x4 at (1, 0)
Solution
y = x2 – x4 at (1, 0)
Differentiating w.r.t. ‘x’
`(("d"x)/("d"y))` = 2x – 4x3
Slope of the tangent ‘m’ = `((dx)/("d"y))(1, 0)`
= 2(1) – 4(1)3
= – 2
Slope of the normal `- 1/"m" = (-1)/(-2) = 1/2`
Equation of tangent is
y – y1 = m(x – x1)
y – 0 = – 2(x – 1)
y = – 2x + 2
2x + y – 2 = 0
Equation of Normal is
y – y1 = `- 1/"m"` (x – x1)
y – 0 = `1/2(x - 1)`
2y = x – 1
x – 2y – 1 = 0
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