If f x is a twice differentiable function such that f 0 = f 1 = f 2 = 0 , then

Question

If f x is a twice differentiable function such that f 0 = f 1 = f 2 = 0 , then, f x = 0 has exactly 3 roots, f ′ x = 0 for atleast 3 real values of x, f ″ x = 0 for atleast 2 real values of x, f ″ x = 0 for atleast 1 real value of x

MARKS App · Accepted Answer

f x = 0 has atleast 3 real roots ∴ By Rolle’s theorem f ′ x = 0 has atleast two real roots and f '' x = 0 has atleast one real root.

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