Explain for which values of a the function a* is increasing and for which values it is decreasing. Use the fact that, for a > 0, (а*) %3D (In a) a'. dx 'We are interested in when the derivative 2 is positive and when it is negative. The quantity a* is always positive. However, In a > 0 for a > 1 and In a < 0 for 0 < a < 1.Thus, the function a* is increasing for a > I and decreasing dx for a < 1. We are interested in when the derivative 2 is positive and when it is negative. The quantity a* is always positive. However, In a > 0 for a > e and In a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing for a < e. d(a") We are interested in when the derivative dx is positive and when it is negative. The quantity In a is always positive. However, a > O for a > 1 and a < 0 for 0 < a < 1. Thus, the function a" is increasing for a > I and decreasing for a < 1. d(a*) dx We are interested in when the derivative However, a > 0 for a > e and a < 0 for 0 < a < e. Thus, the function a* is increasing for a > e and decreasing for a < e. is positive and when it is negative. The quantity In a is always positive.