Hi, Danniella hey Grant.
Okay
a)
y = x^3/2 + 48/x
dy/dx = 3/2x^1/2 - 48x^-2
if dy/dx = 0
3/2x^1/2 - 48x^-2 = 0
3/2x^1/2 = 48x^-2
x^1/2 = 32x^-2
x^1/2/x^-2 = 32
x^5/2 = 32
x^1/2 = 2
x = 4
b)
Sub x = 4 into y = x^3/2 + 48/x
y = 20
x = 4 y = 20
d^2y/dx^2 = 3/4x^1-2 + 96x^-3
sub x = 4 into 3/4x^1-2 + 96x^-3
d^2y/dx^2 = 15/8 therefore minimum.
Grant some rep would be nice :P