Consider the cubic equation x^3 = 3x + 8. If we differentiate each side with respect to x, we obtain 3x^2 = 3, which have two solutions x = 1 and x = −1. But neither of these is a solution of the original cubic equation. Explain what went wrong and why does the differentiation of both sides of the cubic equation gives an invalid result.

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)