Hey everyone! Recently got a question in maths which asks: "Use integral calculus to find the equation of the quartic that has stationary points of inflection at (1, 23) and (3, 15) and a y-intercept of 24" This means that the second derivative has the form (as inflection points are x-intercepts in the second derivative): f''(x) = k(x-1)(x-3) I integrate this and get an answer for f'(x), all fine and dandy. But then I say, since there are two stationary points, f'(1) = 0, and f'(3) = 0, and it all breaks down! Is it even possible to have a quartic with TWO stationary points of inflection, or am I just screwing something up (haha)? Cheers.