Question 565454
Take the derivative of f with respect to x (I used the product rule):


*[tex \LARGE f'(x) = 2(x^2+4)^3 + 12x(x-3)(x^2+4)^2]


Set it equal to zero and find all real x that satisfy. Once you have done this, check to make sure that the sign of f'(x) actually changes.