Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingHard2 minPYQ_2024

MathematicsHardsingle choice

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

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Solution:

Here $\frac{d ^{2} y}{d x ^{2}} = n (n - 1) (x - a)^{n - 2}$ Now, $\frac{d ^{2} y}{d x ^{2}} = 0 \Rightarrow x = a$ Differentiating equation of the curve $n$ times, we get, $\frac{d ^{n} y}{d x ^{n}} = n$ ! $∴$ at $x = a, \frac{d ^{n} y}{d x ^{n}} \neq = 0$ and $\frac{d ^{n - 1} y}{d x ^{n - 1}} = 0$ , where $n$ is odd. Therefore $(a, 0)$ is the point of inflexion

Stream:BITSATSubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Increasing-Decreasing

⏱ 2mℹ️ Source: PYQ_2024

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