Question

Find the point of inflections of the curve

f(x) = x⁴ – 6x³ + 12x² – 8x + 3

Answer 1

We have f(x) = x⁴ – 6x³ + 12x² – 8x + 3

⇒ f'(x) = 4x³ – 18x² + 24x – 8

⇒ f"(x) = 12x² – 36x + 24

= 12(x² – 3x + 2) = 12(x – 1)(x – 2)

Now, f"(x) = 0 gives x = 1, 2

when x = 1, y = 2

when x = 2, y = 3

Thus, the point of inflection are (1, 2) and (2, 3)