Let f ( x ) = ⎩ ⎨ ⎧ ( x + 1 ) 3 x 2/3 − 1 − ( x − 1 ) 2 − 2 < x ≤ − 1 − 1 < x ≤ 1 1 < x < 2 The total number of maxima and minima of f (x) is

f ′ ( x ) = ⎩ ⎨ ⎧ 3 ( x + 1 ) 2 3 2 x − 1/3 − 2 ( x − 1 ) − 2 < x < − 1 − 1 < x < 1 , x  = 0 1 < x < 2 f ′ ( x ) DNE at x = − 1 , 0 , 1 . Sign of f ′ ( x )

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MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

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Let $f (x) = ⎩ ⎨ ⎧ (x + 1)^{3} x^{2/3} - 1 - (x - 1)^{2} - 2 < x \leq - 1 - 1 < x \leq 1 1 < x < 2$

The total number of maxima and minima of f (x) is

Options:

Answer:

Solution:

$f^{'} (x) = ⎩ ⎨ ⎧ 3 (x + 1)^{2} \frac{2}{3} x^{- 1/3} - 2 (x - 1) - 2 < x < - 1 - 1 < x < 1, x \neq = 0 1 < x < 2$

$f^{'} (x)$ DNE at $x = - 1, 0, 1$ .

Sign of $f^{'} (x)$

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

⏱ 2mℹ️ Source: QB

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