Maxima and MinimaHard
Question
If the function f(x) = 2x3 - 9ax2 + 12a2 x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p2 = q, then a equals
Options
A.3
B.1
C.2
D.
Solution
f (x) = 0 at x = p, q
6p2 + 18ap + 12a2 = 0
6q2 + 18aq + 12a2 = 0
f″(x) < 0 at x = p
and f″(x) > 0 at x = q.
6p2 + 18ap + 12a2 = 0
6q2 + 18aq + 12a2 = 0
f″(x) < 0 at x = p
and f″(x) > 0 at x = q.
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