Turning points of the curve y = (9x^2 +1)/3x+2

Use quotient rule to differentiate:

dy/dx = (18x(3x+2) - 3(9x²+1))/(3x+2)²

set dy/dx=0:

54x² + 36x - 27x² - 3 = 0

9x² + 12x - 1 = 0

solve quadratic to obtain values of x, and then find corresponding values of y by subbing these x values into original equation.

To find if max or min, differentiate formula twice, then sub in values of x. If f''x > 0, then minimum. If f''x < 0, maximum.