Fig owns a candy store in a local mall. Each December, Fig only sells holiday samplers. With the help of some business majors on coop from University, Fig has found the following model for her prot function: P(x) = (24.8x 0.2x2 )e''5" where P(x) is the prot in dollars if each sampler is sold forx dollars. Carefully enter the function P(x) into 1'] on your calculator. Check that you have entered the function correctly by computing P(5). You should obtain 9167729319. (a) (6 points) From the past sales experience, Fig knows that the sale price of each sampler should not be more than $30 but she doesn't want to sell sampler for less than $4. Use a derivative and your calculator to determine the price that maximizes prot. Write the answer with all the decimal places the calculator gives. Calculator answer (with units) : (b) (6 points) Show in two different ways that the price you found in part (a) maximizes the prot (0) (2 points) What is the maximum prot? Round to 2 decimal places and give your answer with a unit