A problem

Graph .

First we find  We shall determine the signs of  this is a difficult one to check, but we shall check the signs from both numerator and denominator. Note that the signs of numerator depends on if  or  which means if x>3 or x<3.

(1) We see that f is decreasing in (-1,3) and increasing in 

(2) f has a minimum at x=3, f(3)=-5.

(3) Note that 

(4) Use plot(x - 4*sqrt(x+1), x=-2..3, thickness=3); to check your answer.
 

Mon Nov 18 21:11:38 EST 1996