alleryThe critical points of f(x) = x³ − 3x + 1 are found by solving f'(x) = 0:
A$x = ±1$ (from $3x^2 - 3 = 0$)
B$x = 0$ only (single critical)
C$x = ±2$ (incorrect calculation)
D$x = ±3$ (mistaken derivation)
Answer & Solution
Correct answer: A. $x = ±1$ (from $3x^2 - 3 = 0$)
We have f'(x) = 3x² − 3.
That is f'(x) = 0 → x².
So f'(x) = 1.
→ x = ±1. Critical points at x = 1 (local min, f''(1) = 6 > 0) + x = -1 (local max, f''(-1) = -6 < 0).
Keep practising Continuity, Differentiability & Derivatives
Browse all Continuity, Differentiability & Derivatives questions for AP Intermediate 2nd Year, or explore more Mathematics topics.