The function y = a log x + bx2 + x has extreme values at x = 1 and x = 2. Find a and b.

Q3 of 137 Page 18

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

Find the local extremum values of the following functions:

f(x) = – (x – 1)³(x + 1)²

Show that has a maximum value at x = e

Find the maximum and minimum values of the function .