Maxima and MinimaMedium
Question
If the function f(x) = 2x3 - 9ax2 +12a2x +1 where a > 0, attains it′s maximum and minimum at p and q respectively such that p2 = q then ′a′ equals -
Options
A.1
B.2
C.1/2
D.3
Solution
f(x) = 2x3 -9ax2 +12a2x +1, a > 0
f′(x) = 6x2 -18ax +12a2
= 6(x2 - 3ax + 2a2)
= 6(x - a) (x - 2a)
p = a, q = 2a
⇒ a2 = 2a
⇒ a = 0(rejected) or a = 2
a = 2
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