find the marginal cost function. c(x)=230 + 7.3x - 0.05x^2 c(x)=□

Explanation:

Step1: Recall derivative rules

The derivative of a constant $a$ is $0$, i.e., $\frac{d}{dx}(a)=0$; the derivative of $ax$ is $a$, i.e., $\frac{d}{dx}(ax)=a$; the derivative of $ax^{n}$ is $nax^{n - 1}$ by the power - rule.

Step2: Differentiate each term of $C(x)$

For the constant term $230$, $\frac{d}{dx}(230)=0$. For the term $7.3x$, $\frac{d}{dx}(7.3x)=7.3$. For the term $-0.05x^{2}$, using the power - rule with $n = 2$ and $a=-0.05$, we have $\frac{d}{dx}(-0.05x^{2})=-0.05\times2x=-0.1x$.

Step3: Combine the derivatives of the terms

$C^{\prime}(x)=\frac{d}{dx}(230)+\frac{d}{dx}(7.3x)-\frac{d}{dx}(0.05x^{2})=0 + 7.3-0.1x$.

Answer:

$7.3 - 0.1x$