Let f ( x ) = { ( 3 − sin ( 1/ x )) ∣ x ∣ , 0 , x  = 0 x = 0 . Then at x = 0 , f has a

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MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

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Let $f (x) = {(3 - sin (1/ x)) ∣ x ∣, 0, x \neq = 0 x = 0$ . Then at $x = 0$ , $f$ has a

Answer:

Solution:

$f$ is continuous at $x = 0$ Further $f (0 + h) > f (0)$ and $f (0 - h) > f (0)$ , for positive 'h'.

Hence f has minimum value at $x = 0$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: QB

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