Answer:
$ 1905.52
Step-by-step explanation:
[tex]C(x) = 20000+15xe^{x/700}[/tex]
The marginal cost is the derivative of [tex]C(x)[/tex].
By applying product rule of differentiation (and using the fact the derivative of a constant is 0, thereby ignoring 20000),
[tex]\dfrac{d}{dx}C(x) = x\dfrac{d}{dx}e^{x/700} + e^{x/700}\dfrac{d}{dx}x[/tex]
[tex]M(x) = \dfrac{d}{dx}C(x) = \dfrac{x^2}{700}e^{x/700} + e^{x/700} = e^{x/700}\left(\dfrac{x^2}{700}+1\right)[/tex]
When x = 700,
[tex]M(700) = e^{700/700}\left(\dfrac{700^2}{700}+1\right) = 701e = 1905.52[/tex]
