1. (10%) Find k such that f(x) = kx2 is a probability density function over the interval [2, 5]. Then write the probability density function.

7. (10%) A company's marginal cost function is and fixed costs are 200, where x is a nonnegative real number that denotes the amount of units produced. Find its cost as a function of x. (Hint: Marginal cost is the cost added by producing one additional unit of a product or service.)