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If p(x) be a polynomial of degree three that has local maximum value ‘8’ at x = 1 and local minimum value 4 at
x = 2 then p(0) is equal to

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-24

-12

answer is D.

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Detailed Solution

$p^{1} (x) = a (x - 1) (x - 2) = a (x^{2} - 3 x + 2)$
I. O. B. S
$p^{} (x) = a [\frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x] + b$
p (1) = 8 p (2) = 4
5a + 6b = 48 2a + 3b = 12
a = 24, b = -12
p(0) = b = - 12

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