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Standard XII

Mathematics

Extrema

Does the func...

Question

Does the function $y = x - sin x$ have a maxima or a minima.

maximum exists

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minimum exists

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both maximum and minimum exists`

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neither maximum nor minimum exists

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Solution

The correct option is C neither maximum nor minimum exists
$\frac{d y}{d x} = 1 - c o s x = 0$
Or
$c o s x = 1$
Or
$x = 0, 2 π$ .
Now
$\frac{d^{2} y}{d x^{2}} = s i n (x)$
Now
${\frac{d^{2} y}{d x^{2}}}_{0, 2 π} = 0$ And so on..
Following the nth derivative test we get that there are no extremums,

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Does the function y=x−sinx have a maxima or a minima.

The correct option is C neither maximum nor minimum existsdydx=1−cosx=0Or cosx=1Or x=0,2π.Now d2ydx2=sin(x)Now d2ydx20,2π=0 And so on..Following the nth derivative test we get that there are no extremums,

Does the function $y = x - sin x$ have a maxima or a minima.