Question

Do them ALL or don't do any at all, please. I need ALL of the questions answered not only 1. Also, identify the coordinates of the local maximum and minimum points. Identify the absolute maximum and minimum points and the coordinates of any inflection points, do not graph. Please follow the instructions that I have provided and answer everything that I have asked, really important for me. Thank you!

Identify the coordinates of any local and absolute extreme points and inflection points. Graph the function. - x4 = x? (8 - x) y = 8x3

Answer 1

f(x) = = dra f(x)= y = 8x? - x* = x (8 - x) x-intercepts : x=0.8 Differentiate y = 8x - x* with respect to x = 24x2 - 4x = 4x2 6-x) dx dy f"(x)= = 48x-12x = 12x(4-x) dy =0= 4x² (6-x)=0= x=0,6 dx So x=0,6 are the critical points. f(0) = 0 and f"(0)=0= The graph of f(x) has inflection point at x = 0 At x =6. f"(6)=12x6(4-6)=-144<0 = x=6 is local maximum End behaviors, lim f(x) = lim x (8 - x) = -00 lim f(x) = lim x' (8 - x)=-00 Absolute maximum :x=6 Absolute minimum :x= = DNE The graph of f(x) is shown below: X ++

+ 400 Х f(x) = 8,3 - 1+ 2 x 200 3 -5 0 5 10 -200