Absolute maxima and minima a. Find the critical points of f on the given interval. b. Determine the absolute extreme values of f on the given interval. c. Use a graphing utility to confirm your conclusions. ? ? ? f(? )= ?x2? 10 on [?2. 3]

STEP_BY_STEP SOLUTION Step-1 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 1 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 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 a funct ion withdomain D and let c be afixed constant in D . Then t he output value f (c) 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 -10 , on [-2,3].Clearly the function is polynomial function and it is continuous for all of x . Now , we have to find out the critical points of f on the given interval. 2 Now , f(x) = x -10 then differentiate the function both sides with respect to x. 1 d 2 f (x) = dx ( x -10) = dx ( x ) - dx (10) =...