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JEE Main20244 Apr 2024Evening ShiftMathematicsApplication of DerivativesActual

Let f: R R be a thrice differentiable function such that f(0)=0, f(1)=1, f(2)=-1, f(3)=2 and f(4)=-2 . Then, the minimum number of zeros of (3 f^ f^ +f f^ )(x) is _______

Correct answer

0

Step-by-step solution

aligned & (3 f^ f^ +f f^ )(x)= ( (f f^ + (f^ )^2 )(x) )^ & (f f f^ + (f^ )^2 )(x)= ( (f f^ )(x) )^ & (3 f^ f^ +f^ )(x)= (f(x) f^ (x) )^ aligned aligned & roots of f ( x ) 4 & . roots of f ^ ( x ) 3 & roots of ( f ( x ) f ^ ( x ) ) 7 & roots of ( f ( x ) f ^ ( x ) )^ 5 aligned

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