If f ( x ) = { x 3 sin ( x 1 ) , x  = 0 0 , x = 0 then

f ′ ( x ) = 3 x 2 sin ( x 1 ) − x cos ( x 1 ) f ′′ ( x ) = 6 x sin ( x 1 ) − 3 cos ( x 1 ) − cos ( x 1 ) − x sin ( x 1 ) f ′′ ( π 2 ) = π 12 − 2 π = 2 π 24 − π 2

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Mathematics - Differentiation Question with Solution | TestHub

MathematicsDifferentiationDifferentiation of composite functionsMedium2 minPYQ_2024

MathematicsMediumsingle choice

If $f (x) = {x^{3} sin (\frac{1}{x}), x \neq = 0 0, x = 0$ then

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Answer:

Solution:

$f^{'} (x) = 3 x^{2} sin (\frac{1}{x}) - x cos (\frac{1}{x}) f^{''} (x) = 6 x sin (\frac{1}{x}) - 3 cos (\frac{1}{x}) - cos (\frac{1}{x}) - \frac{sin ( \frac{1}{x} )}{x} f^{''} (\frac{2}{π}) = \frac{12}{π} - \frac{π}{2} = \frac{24 - π ^{2}}{2 π}$

Stream:JEESubject:MathematicsTopic:DifferentiationSubtopic:Differentiation of composite functions

⏱ 2mℹ️ Source: PYQ_2024

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