Question

1. a company’s profit function is: $p(x) = -3x^2 + 60x - 200$ find the marginal profit at $x = 6$. interpret your answer.

1. given the function:

$f(x)=\begin{cases}2x + 3, & x < 1\\x^2 + 1, & x geq 1end{cases}$
find:

• $limlimits_{x \to 1^-} f(x)$
• $limlimits_{x \to 1^+} f(x)$
• $limlimits_{x \to 1} f(x)$

Explanation:

Answer:

1. Marginal profit is $24$. This means that at a production level of $6$ units, the profit is increasing at a rate of $24$ per additional unit produced.
2. $\lim_{x \to 1^-} f(x) = 5$; $\lim_{x \to 1^+} f(x) = 2$; $\lim_{x \to 1} f(x)$ does not exist.