JEE PYQ: Application Of Derivatives Question 26
Question 26 - 2020 (02 Sep Shift 1)
If $p(x)$ be a polynomial of degree three that has a local maximum value $8$ at $x = 1$ and a local minimum value $4$ at $x = 2$; then $p(0)$ is equal to:
(1) $6$
(2) $-12$
(3) $-24$
(4) $12$
Show Answer
Answer: (2)
Solution
$p’(x) = \lambda(x-1)(x-2)$, $\lambda > 0$. $p(x) = \lambda\left(\frac{x^3}{3} - \frac{3x^2}{2} + 2x\right) + C$. $p(1) = 8$ and $p(2) = 4$ give $\frac{5\lambda}{6} + C = 8$ and $\frac{2\lambda}{3} + C = 4$. So $\lambda = 24, C = -12$. $p(0) = C = -12$.
BETA
