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 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) 1 = 0 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 function 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 x 2 , on [- 2, 2].Clearly the function contains the root , the root value is always positive . So , 2 - x 2 0 2 That is , x 2 -2 x 2 Therefore, the given function is continuous on [-2,2] Now , we have to find out the critical points of f on the given interval. 2 Now , f(x) = x 2 x then differentiate the function both sides with respect to x. 1 d 2 f (x) = dx( x 2 x ) d 2 2 d d d d = x dx ( 2 x )+ 2 x dx (x) , sincedx(uv) = u dx(v) + v dx (u) 1 d 2 2 d 1 = x 2 dx (2 -x ) + 2 x (1) ,...