Does the function:
f(x) = 3 + (1/(x+2))
Have any critical (relative max/min) points?
My answer is NO, but I'm not 100% certain this is correct.
The method we were taught is to find the derivative of the function, set it equal to zero, and find the x values. Then we look at intervals to the right and left of this point, and if they are different (pos to neg or neg to pos), then it is a max or min, respectively.
Finding the derivative of this function and setting it equal to zero, then solving for x, yields a result of 1. Finding the derivative of values left and right of this point gives 2 positive answers, meaning that 1 is NOT a critical point, and therefore there are no critical points.
The graph has a vertical asymptote at -2 as the function approaches from the left and the right.
The graph has a horizontal asymptote at 3 as well.
Both of these conditions seem to imply that there are no maximum or minimum points.
Yes? No?