FunctionHard
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
Create a free account to view solution
View Solution FreeMore Function Questions
Let f : R → R be a function defined by f(x) = x + √x2, then f is-...For every pair of continuous functions f, g : [0, 1] →R such that max {f(x) : x ∈ [0, 1]} = max {g(x) : x ...The range of the function f(x) = ex-e-x, is -...The range of the function f(x) = 7-xPx-3, is-...If f(x) = log , when − 1 < x1, x2 < 1, then f(x1) + f(x2) equals-...