For the given cost function 16 sqrt x+x^2/3375
The marginal cost at the production level 1700
The minimal average cost
To find the marginal cost at a particular production level, you will need to take the derivative of the cost function with respect to the production level (x).
Let's find the derivative of the given cost function, which is:
Cost function: C(x) = 16√x + x^2/3375
To find the derivative, let's break down the cost function into two terms:
C(x) = 16√x + x^2/3375
The derivative of the first term, 16√x, can be found using the power rule for differentiation:
d/dx (16√x) = (16 * 1/2 * x^(-1/2))
Applying the power rule, we get:
d/dx (16√x) = 8x^(-1/2)
The derivative of the second term, x^2/3375, can be found using the quotient rule:
d/dx (x^2/3375) = [(2x * 3375) - (x^2 * 0)]/(3375^2)
Simplifying, we get:
d/dx (x^2/3375) = (6750x - 0)/(3375^2)
d/dx (x^2/3375) = (6750x)/(3375^2)
Combining the two derivatives, we get:
C'(x) = 8x^(-1/2) + (6750x)/(3375^2)
Now, let's find the marginal cost at the production level of 1700. To do this, substitute the value of x into the derivative function:
C'(1700) = 8(1700)^(-1/2) + (6750(1700))/(3375^2)
Calculating this expression will give you the marginal cost at the production level of 1700.
As for finding the minimal average cost, you will need to find the minimum point of the average cost function by taking the derivative of the average cost function and setting it equal to zero. However, the average cost function is not given in this question. If you provide the average cost function, I can assist you in finding its minimum point.