The daily cost of producing x high performance wheels for racing is given by the following function, where no more than 100 wheels can be produced each day. What production level will give the lowest average cost per wheel? What is the minimum average cost?
C(x)=0.03x^3-4.5x^2+171x; (0,100]

The production of wheel per day is 74 which gives lowest average cost per wheel.

The minimum average cost is $168.72.

Step-by-step explanation:

Given function of average cost is

Differentiating with respect to x

C'(x)= 0.09 x² -9.0 x+171

Again differentiating with respect to x

C''(x) = 0.18 x -9.0

To find the minimum average cost, first we have to set C'=0.

The function's slope is zero at x=a, and the second derivative at x=a is

Now ,

C'=0

⇒ 0.09 x² -9.0 x+171=0

⇒x = 74.49, 25.50

Therefore at x= 74.49≈ 74, the average cost is minimum.

The production of wheel per day is 74 which gives lowest average cost per wheel.

The minimum average cost

                                                      =168.72

[Assume the average cost is in dollar]

The minimum average cost is $168.72.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for