3. (Derivatives) We will use derivatives to define probability density functions. The deriva- tive of a differentiable function f is defined as f' (x) := lim f (oct h) - f(2) (4) h-0 h (a) Briefly explain why the derivative of a function can be interpreted as an instantaneous rate of change. (b) Use the definition to derive the derivative of the function x2. (c) We would like to approximate a differentiable function f at y using a linear function Ly (x) := ax +b. We set a and b so that f and Ly have the same value and the same derivative at y (i.e., Ly(y) = f(y) and L'y(y) = f'(y)). Give an expression for Ly (a) in terms of y, f(y), and f'(y). (d) Let f(x) = 4x2e". Plot f and L2 between 1 and 3