16. Lola decides to find all local and global extrema for the function f (x) = x + 3x -24x on the interval [-5,6] . Correct her work, below. (Her answer is not complete. What did she forget?) f(x)=x'+3x2 -24x f'(x) exists for all values of x, so the only critical numbers f'(x)=3x2 +6x-24 of f are x = -4 and x =2. f'(-4.1) =1.8 , f'(-3.9) =-1.8 so f(-4) = 80 is a local max f'(x) =3x2+6x-24 =0 f'(1.9) = -1.8 , f'(2.1) =1.8 so f(2) =-28 is a local min f'(x) = 3(x2+2x-8) =0 Since these are the only local max/min, they are also the f' (x) = 3(x+4)(x-2)=0 global max/min, so f(-4) =80 is the global max, and f'(x) =0 at x= -4 and x =2 f(2) =-28 is the global min