If f x-x-a2nx-b2m-1 where m-n -N- then

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Standard XII

Mathematics

First Principle of Differentiation

If f x=x-a2...

Question

If $f (x) = (x - a)^{2 n} (x - b)^{2 m + 1}$ where m.n $\in N$ , then

x = a

is a point of minimum

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x = a

is a point of maximum

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x = a

is not a point of maximum or minimum

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No value of k satisfies the requirement

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Solution

The correct option is C $x = a$ is not a point of maximum or minimum
$f (x) = (x - a)^{2 n} (x - b)^{2 m + 1}$
$f^{'} (x) = (2 m + 1) (x - a)^{2 n} (x - b)^{2 m} + 2 n (x - a)^{2 n - 1} (x - b)^{2 m + 1}$
For maxima or minima,
$f^{'} (x) = 0$
$\Rightarrow x = a, b$
$f^{''} (x) = 2 m (2 m + 1) (x - a)^{2 n} (x - b)^{2 m - 1} + 2 n (2 m + 1) (x - a)^{2 n - 1} (x - b)^{2 m} + 2 n (2 n - 1) (x - a)^{2 n - 2} (x - b)^{2 m + 1}$
$+ 2 n (2 m + 1) (x - a)^{2 n - 1} (x - b)^{2 m}$
$f^{''} (x) = 0 a t x = a$

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Similar questions

Q. For the function f(x) =

x + \frac{1}{x}

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Q. Let

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The absolute maximum & minimum values of functions can be found by their monotonic & asymptotic behavior provided they exist. We may agree that finite limiting values may be regarded as absolute maximum or minimum. For example, the absolute maximum value of

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If f(x)=(x−a)2n(x−b)2m+1 where m.n ∈N, then

If $f (x) = (x - a)^{2 n} (x - b)^{2 m + 1}$ where m.n $\in N$ , then