Let f be the quadratic function f(x)=x2−4x+3 defined for 1≤x≤4.
(a) Calculate all x–values in the open interval (1,4) at which f′(x)=0. These are the only interior points where an extremum could occur.
(b) Evaluate f at each endpoint of the closed interval and at every interior point found in part (a).
(c) Determine the absolute minimum and absolute maximum values of f on [1,4]. State both the x–coordinate and the corresponding function value, and give a brief justification for each choice.