Question

Find the critical points of the function and use the First Derivative Test to determine whether the critical point is a local minimum or maximum (or neither). (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) FX) 23 local minimum X local maximum X- neither Determine the intervals on which the function is increasing or decreasing, (Enter your answers using interval notation Enter EMPTY or for the empty set.) increasing decreasing Submit Answer

Answer 1

given that f(x) = 423 22-3 So f'(x) = 12x²(x²-3) - 2x (4x3) (22-3)2 f(x) = 4x4 - 36x² 2-3)2 -, f'(X) - 9 F - 72 ore 24*1*?+9) and so for critical numbers put f'(x) = 0 Wind 4x4 - 36x20 (2²-32 + aa = -3,0,2 at a=-3 fl-3) = -18 a f "(-3) = 04 - 0.25 at x=0 f(0) = 0 , f(o)=0 at n= 9 4 3) = 18 f(3) = 0.25 & f t : at x = -3, f(-3) <0 & maxima 2-3 f1(3) >0 & minima so local minimum at x = 3 local maximum at x=-3 neight neither at x = 6 increasing on -o-3) U( 3,00) decreasing on (-3,-83) ul 3,0) u (0,5) u (15,3)