f ( x ) = { x 2 ∣ x − 1∣ 0 i f x  = 0 i f x = 0 INCREASES IN

f ( x ) = ⎩ ⎨ ⎧ x 2 x − 1 x 2 1 − x 0 i f x > 1 i f x 1 i f x ∈ ( 0 , 1 ) or x ∈ ( − ∞ , 0 ) f is not differentiable at x = 0 , 1 . f ′ ( x ) > 0 if x ∈ ( 1 , 2 ) or x ∈ ( − ∞ , 0 ) .

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingMedium2 minQB

MathematicsMediumsingle choice

$f (x) = {\frac{∣ x - 1∣}{x ^{2}} 0 i f x \neq = 0 i f x = 0$ INCREASES IN

Options:

Answer:

Solution:

$f (x) = ⎩ ⎨ ⎧ \frac{x - 1}{x ^{2}} \frac{1 - x}{x ^{2}} 0 i f x > 1 i f x < 1, x \neq = 0 i f x = 0, 1$

$f^{'} (x) = {\frac{2 - x}{x ^{3}} \frac{x - 2}{x ^{3}} i f x > 1 i f x \in (0, 1) or x \in (- \infty, 0)$

$f$ is not differentiable at $x = 0, 1$ .

$f^{'} (x) > 0$ if $x \in (1, 2)$ or $x \in (- \infty, 0)$ .

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

⏱ 2mℹ️ Source: QB

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