Question

the cost function, $c(x)$, in dollars for producing $x$ units is given by
$c(x)=0.17x^{2}+25x+650$.

approximate the cost of producing the 24th unit by using the marginal cost.
hint: the marginal cost function gives the approximate cost of the next unit.

$32.82
$1347.90
$33.16
$1314.90

Explanation:

Step1: Find marginal cost function

The marginal cost $C'(x)$ is the derivative of $C(x)$.
For $C(x)=0.17x^2 + 25x + 650$, apply power rule:
$C'(x) = 2\times0.17x + 25 = 0.34x + 25$

Step2: Evaluate at $x=23$

Marginal cost at $x=23$ approximates the 24th unit cost.
$C'(23) = 0.34\times23 + 25$
Calculate $0.34\times23 = 7.82$, then $7.82 + 25 = 32.82$

Answer:

$32.82$