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) ‘ 3×1/3 (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)

$251,250 ?

$289,167 ?

$301,500 ?

$347,000 ?

The board of directors recently evaluated the performance of Ra], the manager of the Rolf Wheeldivision that assembles Rolf Wheels. The assessment of his performance was negative based on anunfavorable deviation from predicted costs in his division. Upon hearing of his negative evaluation,Raj called a meeting with the board to plead his case that the unfavorable deviation inperformance was a result of an increase in the cost of the hub, spoke and rim kit purchased from athird party (a direct material). Variable overhead (machine maintenance and operating costs) is allocated on the basis of machinehours. Fixed overhead (rent) is allocated on the bases of estimated production units. Rolf Wheelsuses the following per unit standards based on historical data from previous years: Direct materials (hub, spoke, and rim kit) $50 per wheelDirect Labor 4 hours per wheel at $10 per hour Fixed Overhead (Rent) $6 per wheelVariable Overhead (Machine Maint.) $1.5 per machine hour Note that all wheels are the same, on average. Raj expected to produce 4,000 wheels in 2012, but actually produced 3,000 wheels. Rolf sold2,500 of the wheels produced in Raj’s division for $350 each. Net income is based on Fullabsorption costing. The standard cost of a hub, spoke and rim kit is $50, but the actual cost of ahub, spoke and rim kit was $65. Raj’s division actually incurred the following costs in 2012: ActualCost Direct Materials (hub, spoke and rim kit) $195,000 Variable overhead (Machine_ $13,000maintenance) Fixed Overhead (Rent) $24,000 Variable Selling and Administrative $77,500 Direct Labor $115,000