Questions: Find the marginal cost function. C(x)=240+7.9 x-0.07 x^2 C'(x)=

Solution Steps

The given total cost function is in the form $C(x) = a + bx - cx^2$, where:

• $a$ represents the fixed cost, which is {a}.

• $b$ represents the variable cost coefficient, which is {b}.

• $c$ represents the coefficient for the quadratic term, which is {c}.

In this scenario, $x$ represents the quantity of goods produced.

The marginal cost function, $C'(x)$, is found by taking the first derivative of the total cost function with respect to $x$. Thus, $$C'(x) = \frac{d}{dx}(a + bx - cx^2) = b - 2cx$$

Substituting the given values into the marginal cost function, we get:

$$C'(x) = 7.9 - 2\cdot0.07\cdot50 = 0.9$$

Final Answer: