A curve with equation in the form of y = ax + b/x

y = ax + b/x^{2} has a stationary point at (3 , 4), where a and b are constants. Find the value of a and of b.

X = 3 y = 4

4 = 3a + b/a —–(1)

Y = ax + bx^{-2}

dy/dx = a – 2bx^{-3}—–(2)

sub dy/dx = 0, x = 3 into (2)

0 = a – 2b(3)^{-3}

0 = a – 2b/27—–(3)

Sub (3) into (1)

4 = 3(2b/27) + b/9

4 = 1/3b

b = 12 , a = 2(12)/27

b = 12 , a = 8/9