Solved: Critical points of functions with unknown

Solution 57E 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 a). The given function is f(x) = xx a . Clearly the function contains the root value So , x - a 0 That is , x a Therefore , x belongs to [a, ) Therefore, the given function is continuous on [a, ). Now , we have to find out the critical points of f on the interval. Now , f(x) = xx a for the critical points , we have to differentiate the function both sides with respect to x. d d dx f(x) = dx( x x...