Homework Help 20-28

5. 9'(2) = 2x f (2) + x2f'(x) - 1 022 10.0 points x vac Find the value of 6. g'(2) = 2x f (20) + x2 f'(x) -1 Vx lim f (z) - f(3) x-3 0 10.0 points Vx - V3 Find all values of x at which the tangent whenever f is a differentiable function. line to the graph of 1. limit = -f'(3) 2-2 y = x + 5 2. limit = f'(3) is horizontal. 1. x = -10 3. limit = 2V3 f'(3) 2. x = -10, 0 4. limit = -2 f'(3) 3. x = -5, 0 5. limit = 2 f'(3) 4. x = 0 6. limit = -2V/3 f'(3) 5. x = 9 023 10.0 points 6. x = 9, 0 Find the derivative of 7. x = -5 f (x) = (2 - 8) |2-81. 021 10.0 points Find equations for those tangent lines to 1. f'(x) = 12x -81 the graph of y = x + 2 2. f'(x) = 2|2 -81 that are parallel to the line y + 2x = 3. 3. f'(x) = 2x - 8 1. y + 2x - 5 =0, y+ 2x+3=0 4. f'(2) = 12 - 81 2. y + 2x - 5 =0, y+ 2x+6=0 5. f'(2) = 2(x -8) 3. y + 2x - 2 =0, y - 2x+3=0 6. f'(x) = x-8 024 10.0 points 4. y - 2x - 2 =0, y - 2x+6=0 Values of m and b can be chosen so that the 5. y + 2x - 2 =0, y+ 2x+3=0 function 32+ 7, 252, 6. y - 2x - 5 =0, y+2x+6=0 f (20 ) = mac + b , x > 2 ,is differentiable for all values of x. What is the value of m? 5. p(a) = 4-2x2 1. m = 12 027 10.0 points 2. m = 1 If Q is a degree 3 polynomial such that 3. m = 7 Q(1) = -1, Q'(1) = -1, Q"(1) = 2, Q"(1) = 12, 4. m = find the value of Q(-1). 5. m = 9 1. Q(-1) = -8 025 10.0 points 2. Q (-1) = -7 Determine F'(x) when 3. Q(-1) = -10 F (2) = 2xf'(2) +3f(x) and f is a twice-differentiable function. 4. Q(-1) = -9 1. F'(x) = 5 f'(x) + 2x f"(x) 5. Q(-1) = -11 2. F'(x) = 5f'(x) +3x f"(x) 028 10.0 points 3. F'(x) = - f'(2) - 2 x f"(2) Find the derivative of f when 4. F'(x) = 5f'(x) - 3x f"(x) f (2) = I-3 2 - 1 5. F'(x) = - f'(2) - 32 f"(x) 6. F'(2) = - f'(2) + 2 2 f"(2) 1. f'(x) = 3-x (2 -x)2 ex-3 026 10.0 points 2. f' (a) = 3+x 2 - x I-3 Determine p(x) so that 3. f'(a) = 7 ex-3 = p(a) (2 -2)2e (202 + 2) 3 4. f' (a) = 1 -x (2 -2)2et-3 1. p(x) = -12 - 6x2 5. f'(a) = 1+x 2 - x - ex-3 2. p(x) = 4-6x2 6. f'(a) = 3 (2 - 2)2 et-3 3. p(x) = 6 -20x2 4. p(2) = 4+24x2