Question

Find the point of inflection of the curve y = f(x) = (x – 2)^2/3 + 10

Answer 1

We have y = f(x) = (x – 2)^2/3 + 10

⇒ f'(x) = 2/3(x – 2)^{– 1/3} = 2/3(x – 2)^1/3

⇒ f"(x) = 2/9(x – 2)^4/3

Thus, f"(x) does not exist at x = 2.

when x = 2, y = 0 + 10 = 10

Thus, the inflection point is (2, 10)