use differential approximations in the following problem. a company will sell n units of a product after…

use differential approximations in the following problem. a company will sell n units of a product after spending $x thousand in advertising, as given by n = 50x - x², 5 ≤ x ≤ 25. approximately what increase in sales will result by increasing the advertising budget from $15,000 to $16,000? from $20,000 to $21,000? find the differential dn. dn = ( )dx the increase in sales from increasing the advertising budget from $15,000 to $16,000 is approximately ( ) units. (type a whole number.) the increase in sales from increasing the advertising budget from $20,000 to $21,000 is approximately ( ) units. (type a whole number.)

use differential approximations in the following problem. a company will sell n units of a product after spending $x thousand in advertising, as given by n = 50x - x², 5 ≤ x ≤ 25. approximately what increase in sales will result by increasing the advertising budget from $15,000 to $16,000? from $20,000 to $21,000? find the differential dn. dn = ( )dx the increase in sales from increasing the advertising budget from $15,000 to $16,000 is approximately ( ) units. (type a whole number.) the increase in sales from increasing the advertising budget from $20,000 to $21,000 is approximately ( ) units. (type a whole number.)

Answer

Explanation:

Step1: Differentiate N with respect to x

Given $N = 50x - x^{2}$, using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$, we have $\frac{dN}{dx}=50 - 2x$. Then $dN=(50 - 2x)dx$.

Step2: Calculate increase in sales for $x$ from 15 to 16

Here $x = 15$ and $dx=1$. Substitute $x = 15$ into $dN=(50 - 2x)dx$. So $dN=(50-2\times15)\times1=(50 - 30)\times1 = 20$.

Step3: Calculate increase in sales for $x$ from 20 to 21

Here $x = 20$ and $dx = 1$. Substitute $x = 20$ into $dN=(50 - 2x)dx$. So $dN=(50-2\times20)\times1=(50 - 40)\times1=10$.

Answer:

$dN=(50 - 2x)dx$ 20 10