Let f be a real polynomial of degree n such that f(x)=f'(x)f''(x), for all x. If f(0)=0, then 36(f'(2)+f''(2)+∫₀² f(x) dx) is equal to:

Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

JEE Main 2026 · 4 Apr, Morning shift · Q17

JEE Main 20264 Apr, Morning shiftMathematicsEasyLimit, Continuity and Differentiability420× since 2002

Let

f

be a real polynomial of degree

n

such that

f(x)=f'(x)f''(x)

, for all

x\in\mathbb{R}

. If

f(0)=0

, then

36\left(f'(2)+f''(2)+\int_0^2 f(x)\,dx\right)

is equal to: