Question

For the function $f(x) = x^3 - 6x^2 + 12x - 3$, $x = 2$ is:}

• A. A point of minimum
• B. A point of inflection
• C. Not a critical point
• D. A point of maximum

Answer 1

The Correct Option is B

Find $f'(x)$ and $f''(x)$: \[ f'(x) = 3x^2 - 12x + 12, \quad f''(x) = 6x - 12. \] At $x = 2$: \[ f'(2) = 0, \quad f''(2) = 0. \] Check $f'''(x)$: \[ f'''(x) = 6 \implies f'''(2) = 6 \neq 0. \] Thus, $x = 2$ is a point of inflection.