JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q73

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MathematicsSingle correct+4 / -1Question 73 of 90

Let $f$ be a polynomial function such that $f(3x)=f'(x)\cdot f''(x)$ , for all $x\in\mathbb R$ . Then :

f(2)+f'(2)=28

f''(2)-f'(2)=0

f''(2)-f(2)=4

f(2)-f'(2)+f''(2)=10

Answer and worked solution

Official answer: B

Degrees: $n=(n-1)+(n-2)$ gives $n=3$ . Comparing coefficients of $f(3x)=f'(x)f''(x)$ with $f=ax^3+bx^2+cx+d$ : $27a=18a^2$ gives $a=\frac32$ , and then $b=c=d=0$ . So $f=\frac32x^3$ , $f'(2)=18$ and $f''(2)=18$ : $f''(2)-f'(2)=0$ .

Topics:Derivatives of standard functions

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 73