Let f be real function defined on {R} (the set of real numbers) such that f^{'}(x)=100(x-1)(x-2)^{2}(x-3)^{3} . . . . . .(x-100)^{100}, for all x \in R . If g is a function defined on {R} such that \int_{a}^{x} e^{f(t)} d t=\int_{0}^{x} g(x-t) d t+2 x+3, If some of the all the values of {x} for which {g}( {x}) has a local extremum be \lambda then find \frac{\lambda}{3}

JEE Advanced 2020 Full Test 2 Paper 2

Question : 51 of 54

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Let f be real function defined on R (the set of real numbers) such that f′(x)=100(x−1)(x−2)2(x−3)3......(x−100)100, for all x∈R. If g is a function defined on R such that

∫

ef(t)dt=

∫

g(x−t)dt+2x+3, If some of the all the values of x for which g(x) has a local extremum be λ then find ‌

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