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,

i will pick c put check it over to be sure

step-by-step explanation: