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

Solution :

f(x) = \(3x^4 – 4x^3\)

f'(x) = \(12x^3 – 12x^2\)

f'(x) = \(12x^2(x – 1)\)

Now, f”(x) = \(12(3x^2 – 2x)\)

f”(x) = 12x(3x – 2)

f”(x) = 0  \(\implies\)  x = 0, 2/3

Here, f”(x) = 0

Thus, x = 0, 2/3 are the inflection points.

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