Part A) Find all Relative Extrema and show work and Part B) Find all Critical Numbers and show work Solution As for all real x, (x+1)^2 is always positive => -1/(x+1)^2 is always negative dy/dx = -ve means the function y = f(x) decreases continuously similarly, dy/dx = +ve means the function y = f(x) increases continuously in this case it is always negative therefore the value of function decreases continuously from -infinity to +infinity => no extrema.

1. Part A) Find all Relative Extrema and show work
and Part B) Find all Critical Numbers and show work
Solution
As for all real x,
(x+1)^2 is always positive
=> -1/(x+1)^2 is always negative
dy/dx = -ve means the function y = f(x) decreases continuously
similarly,
dy/dx = +ve means the function y = f(x) increases continuously
in this case it is always negative
therefore the value of function decreases continuously from -infinity to +infinity
=> no extrema