Abs. Max/min on a guven interval

Question

f(x)= (x^2)/(x^2+1) [ 1,2] 

 

Its saying that the abs min is (2,4/5) and max is (1,1/2) . I dont understand isnt it supposed to be the opposite. Shouldnt the max be (2, 4/5) ? Isnt 0.8 bigger than 0.5 ?

Answer 1

First, set the derivative of f(x) equal to zero.  Then, solve for x from the derivative equation to get your critical points (c).  Then evaluate f(x) at x=c.

 

Finally, evaluate f(1), f(c), and f(2).  The lowest of these f(x) values is the absolute minimum.  The highest of these f(x) values is the absolute maximum.

 

 

Got it?

Answer 2

Those are reversed