You are asked to come up with a piecewise function f(x) that includes a maximum of four functions that satisfy the following conditions and then provide a Desmo graph of this piecewise function. The four pieces of function must be expressed algebraically. Conditions: i. lim f(x) exists where -8 Create a quadratic function using the form f(x) = ax+bx+c in the interval of [p.q], such that f(p)= f(a) and a,b,c*0 A. Find the derivative function expression for your created quadratic using the first principle. B. Determine the average rate of change in the interval [p.q]. C. Sketch the quadratic for the portion of the interval [p.q] and the secant line described in part B. D. From the graph, determine point where the instantaneous rate of change on this quadratic will be the same as the average rate of change you found in part B. E. Determine this point algebraically.