Question

2. Given f(x) = find the derivative using the definition of derivative. 3. Find A and B given that the function, f(x), is continuous at x = 6. V | f(x) = {B (Ar - 42 > 6 4. Find the slope of the tangent line to the curve 2.2 - 2xy + 3y2 = 10 at the point (1,2).

Answer 1

1 Given, 8(x) = Tie f'w = (HX+)(0) - 0) (H) (4&to 2 Cheat 2 - (4x+1)

6x² ; x<6 Given, f(x) is continuous at 6: f(x) = 2 B ; 2=6 LAX=42; 876 * as f(x) is continuous at it + Xe ben fo) - him f(n) = f(6) - ( xs) ay bin tox-] =B (6)² = A(6)-H2 =B. → 136 =6A-42 = B 10 from I $B=36 and 6A-42=36 6A=36th 2 => A=78 - 13 =>JA=13 A=13 and B=36.

Given, zx²2xy + 3y =10 => fca, y) = 2x22xy +39?-16 =o. Given point is (1, 2) "Slope of tangent is, fx = 41-24 fy = -2x+64 - Chex-2y) 1 - (Hex- - -(he) - 2(2))] 3) = 200) +6 (2) [-2x+6y at (82) = -(4-4) - 2 + 12 My = 0 Slope of tangent is mr zo]