Suppose that f(x) = x2/3(x 8)1/3. You should be able to determine f'(x) and f(x) for this function, but I am providing them so you can finish...

i need help for this example problem and to understand the next lesson , thank you

Suppose that f(x) = x2/3(x — 8)1/3. You should be able to determine f'(x) and f"(x) for this function, but I am providingthem so you can finish all parts ofthis problem. No need to recalculate them. 9’ , _ 3x — 16f (x) ‘ 3x1/3 (x — 292/3 H _ —128f (x) _ 9354/30: _ 8)5/3 Find the (any) coordinates of all x and y intercepts. (2 pts)Determine the critical numbers off. Be careful. (6 pts)Find the interval(s) on which f is increasing and those on which f is decreasing.(4 pts)Find the (x, y) coordinates of all local extreme points. Be sure to say what type ofextreme point it is, and to justify your answer. (4 pts)Find the interval(s) on which f is concave up and those on which f is concave down.(4 pts)Find the (x, y) coordinates of all points of inflection. Be sure to justify that eachpoint you determine is a point of inflection. (5 pts)Graph the function. (5 pts)