If `y = (a+bx^(3/2))/x^(5/4) & (dy)/(dx)` vanishes when `x = 5` then `a/b` is

Options

A. `sqrt(5) : 1`
B. `5 : 1`
C. `3 : 5`
D. `1 : 2`

Answer

A

Explanation

`y = (a+bx^(3//2))/(x^(5//4))`
On differenting, we get
`y' = ((3)/(2)bx^(7//4)-(5)/(4) (a+bx^(3//2))x^(1//4))/((x^(5//4))^(2))`
`because y' = 0 at x = 5`
`therefore (3)/(2) bx^(7/4) - (5)/(4) (a + bx^(3//2)) x^(1//4) = 0`
at x = 5
`rArr 6bx^(3//2) -5(a+bx^(3//2)) = 0`
at x = 5
`rArr bx^(3//2) = 5a at x = 5`
`rArr b(5)^(3//2) = 5a`
`rArr (a)/(b)=(5^(3//2))/(5) rArr a:b = sqrt(5) :1`