Solve the following problems. Draw by hand the graphs of each problem complete with labels. Submit the solutions all in handwritten form on clean sheets of pat-er. 1. Make the parabola y = ax: + in: + c pass through [51] and tangent to the line 9:: + 2}: = 12 at [2. -3}. 2. Find the equations of the lines that are tangent to and normal to the curve I I\")?! = 9 at {1.3}. For the given funciion: x) = 2x3 + 9x2 2+: 1i] 3. Determine the local maxima andfor minima. 4. Determine the intervals for which the function is increasing or decreasing. I'll. For the given function: f(x] = {1-1332 5. Determine the inecti on pointqs} 6. Determine the intervals for 1which the funclion is concave upward andjl'or concave downward