Applications of Derivatives

⭐ Important Questions

1. Find equation of tangent to curve y = x² - 2x + 1 at x = 2.
   Show Solution

   y(2) = 4-4+1 = 1. Point: (2,1)\ndy/dx = 2x-2. At x=2: slope = 2\nEquation: y-1 = 2(x-2) => y = 2x-3
2. Find maxima/minima of f(x) = x³ - 6x² + 9x + 1.
   Show Solution

   f'(x) = 3x² - 12x + 9 = 3(x²-4x+3) = 3(x-1)(x-3)\nCritical: x=1, x=3\nf''(x)=6x-12. f''(1)=-6 max at x=1, f=5\nf''(3)=6 > 0 => min at x=3, f=1