Answer:
The marginal cost at the given production level is $49.9.
Step-by-step explanation:
The marginal cost function is expressed as the first derivative of the total cost function with respect to quantity (x).
We have that the cost function is given by
![C(x) = 15000 + 50x + \frac{1000}{x}](https://tex.z-dn.net/?f=C%28x%29%20%3D%2015000%20%2B%2050x%20%2B%20%5Cfrac%7B1000%7D%7Bx%7D)
So, we need the derivative and then we’ll need to compute the value x = 100 of the derivative.
![C'(x)=\frac{d}{dx}\left(15000+50x+\frac{1000}{x}\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\C'(x)=\frac{d}{dx}\left(15000\right)+\frac{d}{dx}\left(50x\right)+\frac{d}{dx}\left(\frac{1000}{x}\right)\\\\C'(x)=0+50-\frac{1000}{x^2}\\\\C'(x)=50-\frac{1000}{x^2}](https://tex.z-dn.net/?f=C%27%28x%29%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%2815000%2B50x%2B%5Cfrac%7B1000%7D%7Bx%7D%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%2FDifference%5C%3ARule%7D%3A%5Cquad%20%5Cleft%28f%5Cpm%20g%5Cright%29%27%3Df%5C%3A%27%5Cpm%20g%27%5C%5C%5C%5CC%27%28x%29%3D%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%2815000%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%2850x%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cfrac%7B1000%7D%7Bx%7D%5Cright%29%5C%5C%5C%5CC%27%28x%29%3D0%2B50-%5Cfrac%7B1000%7D%7Bx%5E2%7D%5C%5C%5C%5CC%27%28x%29%3D50-%5Cfrac%7B1000%7D%7Bx%5E2%7D)
When x = 100, the marginal cost is
![C'(100)=-\frac{1000}{100^2}+50\\\\C'(100)=\frac{499}{10}=49.9](https://tex.z-dn.net/?f=C%27%28100%29%3D-%5Cfrac%7B1000%7D%7B100%5E2%7D%2B50%5C%5C%5C%5CC%27%28100%29%3D%5Cfrac%7B499%7D%7B10%7D%3D49.9)
5a^2 - 6a -4 - (<span>-7a^2 + 3a -9)
=</span>5a^2 - 6a -4 + 7a^2 - 3a + 9
=12a^2 - 9a + 5
answer
12a^2 - 9a + 5
Answer:
7 and 8 because 52 is between 49 and 64
Step-by-step explanation:
Answer:
(g+f)(x)=(2^x+x-3)^(1/2)
Step-by-step explanation:
Given
f(x)= 2^(x/2)
And
g(x)= √(x-3)
We have to find (g+f)(x)
In order to find (g+f)(x), both the functions are added and simplified.
So,
(g+f)(x)= √(x-3)+2^(x/2)
The power x/2 can be written as a product of x*(1/2)
(g+f)(x)= √(x-3)+(2)^(1/2*x)
We also know that square root dissolves into power ½
(g+f)(x)=(x-3)^(1/2)+(2)^(1/2*x)
We can see that power ½ is common in both functions so taking it out
(g+f)(x)=(x-3+2^x)^(1/2)
Arranging the terms
(g+f)(x)=(2^x+x-3)^(1/2) ..