Question

the curve y=ax+ b/x has a relative minimum at the point (1,4). find the values of a and b.

please help. I have no idea how to solve this.

Answer 1

First of all, since (1,4) is on the curve,
4 = a + b

dy/dx = a - b/x^2
= 0 for a max or min

but we are told that this is true when x = 1
so a - b/1 = 0
a - b = 1

add them,
2a = 5
a = 5/2
sub back into the first equation,
a+b=4
5/2 + b = 4
b = 3/2

a = 5/2 , b = 3/2