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BITSAT 2024Paper 1
Exam
BITSAT
Year
2024
Paper
Paper 1
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2024 · Paper 1 · Mathematics · Application of Derivatives

The point of inflexion for the curve y=(x-a)^n , where n is odd...

The point of inflexion for the curve y=(x−a)ny=(x-a)^n, where n is odd integer and n≥3n \geq 3 is

Options

  1. A(a,0)(a, 0)
  2. B(0,a)(0, a)
  3. C(0,0)(0,0)
  4. DNone of these

Correct answer

A. (a,0)(a, 0)

Step-by-step solution

Here d2ydx2=n(n−1)(x−a)n−2\frac{d^2 y}{d x^2}=n(n-1)(x-a)^{n-2} Now, d2ydx2=0⇒x=a\frac{d^2 y}{d x^2}=0 \Rightarrow x=a Differentiating equation of the curve nn times, we get, dnydxn=n\frac{d^n y}{d x^n}=n ! ∴\therefore \quad at x=a,dnydxn≠0x=a, \frac{d^n y}{d x^n} \neq 0 and dn−1ydxn−1=0\frac{d^{n-1} y}{d x^{n-1}}=0, where nn is odd. Therefore (a,0)(a, 0) is the point of inflexion
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