Find the point of inflection for the curve y = \(x^3 – 6x^2 + 12x + 5\).

Solution :

y = \(x^3 – 6x^2 + 12x + 5\)

y’ = \(3x^2 – 12x + 12\)

y” = \(6x – 12\)

y” = 0 \(\implies\) 6x – 12 = 0

\(\implies\)  x = 2

Since, y” = 0 at x = 2,

Hence the point of inflection is 2.

---

Similar Questions

Prove that the function f(x) = \(x^3 – 3x^2 + 3x – 100\) is increasing on R

Separate \([0, {\pi\over 2}]\) into subintervals in which f(x) = sin 3x is increasing or decreasing.

Find the point of inflection for f(x) = \(x^4\over 12\) – \(5x^3\over 6\) + \(3x^2\) + 7.

Prove that \(f(\theta)\) = \({4sin \theta\over 2 + cos\theta} – \theta\) is an increasing function of \(\theta\) in \([0, {\pi\over 2}]\).

Find the inflection point of f(x) = \(3x^4 – 4x^3\).