cost The marginal cost of a product is modeled by (d C)/(d x)=(12)/(√(12 x+1)) When x=13, C=100

step 1 Hello, the cost of the marginal cost of the product modeled by DC by DX, DCYDX, that is equals t

Cost The marginal cost of a product is modeled by (d C)/(d...

cost The marginal cost of a product is modeled by $\frac{d C}{d x}=\frac{12}{\sqrt[3]{12 x+1}}$
When $x=13, C=100$
(a) Find the cost function.
(b) Use a graphing utility to graph $d C / d x$ and $C$ in the same viewing window.

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Key Concepts

Graphing Functions

Graphing functions, including both the cost function and its derivative, is a key method for visualizing the behavior of the system. It helps illustrate the relationship between the cost and production level, as well as the rate of change of the cost.

Marginal Cost

Marginal cost represents the rate at which the total cost changes with respect to the production of one additional unit. It is the derivative of the cost function and provides insight into the incremental cost associated with production changes.

Integration as the Antiderivative

The process of integration is used to find the original cost function from the marginal cost function by determining the antiderivative. This step involves finding a function whose derivative is the given marginal cost expression.

Initial Value Problem

When an initial condition is provided, such as a known cost for a specific production quantity, it allows for the determination of the constant of integration. This step ensures that the derived cost function accurately reflects the given data.

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