Suppose that f:(a, b) R is differentiable and bounded. Moreover suppose that the limits x a f(x) and x b f(x) do not exist.
Prove that, for any alpha in R there is a point c in (a, b) such that f'(c) = α.

Can someone pls ! pls answer all. no explanation needed..

Average acceleration: i have no idea how to do this.

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)