Question

C++ program to find inflection point of curve given coordinates

Answer 1

Let C be the curve in question. C has a local max at (2, 4) if y'(2) = 0 :

First y(2) = 4 ==> 8a + 4b + 2c + d = 4. Second y'(2) = 0 ==> 12a + 4b + c = 0. C has an

inflection point at (0,0) means: y''(0) = 0 ==> 2b = 0. So b = 0. Also (0,0) is on C so:

y(0) = 0 ==> d = 0. So: 8a + 2c = 4 and 12a + c = 0 ==> a = -1/4 and c = 3. So:

(a, b, c, d ) = (-1/4, 0, 3, 0).