Find the cost function if the marginal cost function is given by c'(x)=x^2/5+8 and 32 units costs $381

The marginal cost function is given by:

              ......[1]

Now, we can find the cost function by taking the antiderivative :

               ......[2]

Substitute [1] in [2] we get;

Integration formulas:

then;

 where is constant

Simplify:

             ......[3]

It is also given that for 32 units costs is $ 381

substitute the value of x = 32 and C(x) = $ 381, in [3] to find the constant term

or

or

Simplify:

Substitute this value in [3] we get;

Therefore, the cost function is,

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

answer: 2530

hope this