Question

If y = alog|x| + bx² + x has its extremum values at x = –1 and x = 2, then ______.

Options

• a = 2, b = –1

• a = 2, b = `(-1)/2`

• a = –2, b = `1/2`

• a = –2, b = `(-1)/2`

Answer 1

If y = alog|x| + bx² + x has its extremum values at x = –1 and x = 2, then `underlinebb(a = 2, b = (-1)/2)`.

Explanation:

y = alogx + bx² + x; x ≥ 0

alog(–x) + bx² + x; x < 0

y' = `a/x + 2bx + 1` = 0

`(2bx^2 + x + a)/x` = 0

⇒ Put x = –1 and x = 2

a + 2b = 1  ....(i)

8b + a = –2  ....(ii)

Solving (i) and (ii)

b = `-1/2`

a = 2