Absolute maxima and minima a. Find the critical points of f on the given interval. b. Determine the absolute extreme values off on the given interval. c. Use a graphing utility to confirm your conclusions.

STEP_BY_STEP SOLUTION Step-1 Critical value definition ; Let f be a continuous function defined on an open interval containing a 1 number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) = 0 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 Absolute extreme value 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 be afunction with domain D and let 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 x a). The given function is f(x) = 2 on (-2,2) . Clearly the function is a rational function 4x and here the denominator is not equal to zero . So , 2 - x 2 > 0 2 That is , x < 2 Therefore , -2 < x< 2. Therefore, the given function is continuous on (-2,2) Now , we have to find out the critical points of...