1. Given that b and c are some nonzero constants, consider the following function: y = f (x) = r' +br'+c (a) Find all the extreme points. (b) Find the inflection points of this function: 2. Given that A is a positive constant, consider the following function: f(z) = 3000 r ', r > 10 (a) Calculate the following integral: (b) Calculate the following integral: (c) Calculate the following integral: 3. Consider the following function: z = f(z, y) = e-?" (3 - y) (a) Calculate the first order partial derivatives of f(r, y) with respect to r and y. (b) Calculate the second order partial derivatives of f(r, y) with respect to a and y. (c) Write down the differentials for f(x, y) with respect to r and y