The function y = a log x + bx2 + x has extreme values at x = 1 and x = 2. Find a and b.
we have
y = a log x + bx2 + x
And
For maxima and minima,
Given that extreme value exist at x = 1, 2
a + 2b = – 1 ……(1)
a + 8b = – 2 …… (2)
solving (1) and (2) we get
a = – 2/3 b = – 1/6