Absolute maxima and minima a. Find the critical points off on the given interval. b. Determine the absolute extreme values off on the given interval. c. Use a graphing utility to confirm your conclusions. ? ? ? f(?x) = (?x ? 2)1/2; [2, 6]

STEP_BY_STEP SOLUTION Step-1 Critical point definition ; Let f be a continuous function defined on an open interval containing a number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) 1 1 = 0 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 Absolute extreme values definition; When an output value of a function is a maximum or a minimum over the entire domain of the function, the value is called the absolute maximum or the absolute minimum. Let f be afunction with domain D and let c be a fixed constant in D . Then the output value f( ) is the 1. Absolute maximum value of f on D if and only if f(x) f(c) , for all x in D. 2. Absolute minimum value of f on D if and only if f(c) f(x) , for all x in D. Step_3 a). The given function is f(x) = (x 2) 1/2 , on [2, 6].Clearly the function is root function and it is continuous for all (x-2) 0 .That is x 2. Now , we have to find out the critical points of f on the given interval. 1/2 Now f(x) = (x 2) , for the critical points we have to differentiate the function both sides with respect to x....