FunctionMedium
Question
Consider a function y = f(x) such that 
= x2 & f(1) = 0, then-
= x2 & f(1) = 0, then-Options
A.f(x) is monotonic function
B.f(x) has exactly one maxims & one minims
C.Area bounded by y = f(x) & x - axis is 
sq. units
sq. unitsD.Number of zero′s of equation f(x) = 0 is 2.
Solution
Apply L′Hopitals rule on L.H.S.
⇒
= x2
⇒ f(x) - xf′(x) = - 2x3
⇒ f′(x) -
= 2x2
I.F = e
⇒ f(x).
= 
2x2. dx
f(x) = x3 + cx
∵ f(1) = 0 ⇒ f(x) = x3 - x
⇒
= x2⇒ f(x) - xf′(x) = - 2x3
⇒ f′(x) -
= 2x2I.F = e
⇒ f(x).
= 2x2. dxf(x) = x3 + cx
∵ f(1) = 0 ⇒ f(x) = x3 - x
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