Suppose that \( f(x)=(1+5 x) e^{4 x}\). a. Find all critical numbers of \( f \).(If there are multiple values, enter them separated by commas. If there are no critical points, enter DNE.)\[ x=\] b. Use interval notation to indicate where \( f \) is increasing. (If there are multiple intervals, enter them separated by commas.) c. Use interval notation to indicate where \( f \) is decreasing. (If there are multiple intervals, enter them separated by commas.) d. List the x-coordinates of all local maxima of \( f \).(If there are multiple values, enter them separated by commas. If there are no local maxima, enter DNE.)\[ x=\] e. List the x -coordinates of all local minima of \( f \).(If there are multiple values, enter them separated by commas. If there are no local minima, enter DNE.)\[x=\]f. Use interval notation to indicate where \( f \) is concave up.(If there are multiple intervals, enter them separated by commas.)g. Use interval notation to indicate where \( f \) is concave down. (If there are multiple intervals, enter them separated by commas.)h. List the \( x \)-values of all inflection points of \( f \).(If there are multiple values, enter them separated by commas. If there are no inflection points, enter DNE.)\[x=\]