with detailed solution handwritten neat and clean homogeneous and variable separable

1. Find the equation of the tangent line and the normal line to the graph of y = v6x - 2 at x = 3. Graph the function and its derivative. (8 points) 2. Find Dx ). Show another solution using product rule. Reconcile your answers. (6 points) 3. Kate and Sarah are working on taking the derivative of f(x) = = 2x 3x+4 Kate uses the quotient rule to get, f'(x) = (3x+4) 2-2x (3) 8 (3x+4)2 (3x+4)2 Sarah converts it into a product and uses the product rule and the chain rule: f(x) = 2x(3x + 4)-1 f'(x) = 2x(-1)(3x + 4)-2(3) +2(3x +4)-1 = 2(3x + 4)-1 - 6x(3x + 4) -2 . Explain the discrepancies between the two answers. Which procedure do you think is preferable? Explain. Answer should be in 3-5 sentences. (4 points) 4. Find the error/s in the solution by encircling that part/those parts of the error/s in red ink and write/show the complete correct solution. (4 points) (2x+5)(2x)-(x2-1)2 _4x2+10x-2x2+2 (x2-1)2 (x2-1)2 2x2+10x+2 (x2-1)2 5. Find the equation of the tangent line and the normal line to the curve f(x) = =x2 -;x+ at the x -intercept closest to the origin. Support your answer graphically by showing the graph of f(x) and the obtained tangent and normal line. Show your complete solution and label the graph properly. (8 points)