Curve sketching and concavity
Differentiation · Mathematics
Study notes
Q: Sketch y = x^3 - 3x^2 using concavity. f'(x) = 3x^2-6x = 0 at x=0,2 (max at 0, min at 2). f''(x) = 6x-6 = 0 at x=1: concave down left, up right. Inflection (1,-2). Intercepts: x^2(x-3)=0: x=0,3. Passes (0,0) max, (1,-2) inflection, (2,-4) min, (3,0).