3. Consider the following income tax scheme: 1) The first $5,000 of income is not subject to any tax. 2) The next $15,000 is subject to a tax rate of 20%. 3) The next $30,000 is subject to a tax rate of 35%. 4) Any additional income is subject to a tax rate of 50%. a. Find the tax function, T(y), defined on y 2 0. b. Determine the points of nondifferentiability for this function and indicate, according to the definition on slide 18 in the Chapter 5 PowerPoint on Moodle, why each is a point of nondifferentiability. c. Find the marginal tax function and the average tax function, T ( y)