the revenue (in dollars) from the sale of x car seats for infants is given by the following function…

the revenue (in dollars) from the sale of x car seats for infants is given by the following function. r(x)=28x - 0.010x^2 0≤x≤2800 (a) find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (b) use the four - step process to find r(x). (c) find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (a) find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. 7.5 (round to one decimal place as needed.) (b) r(x)=□

the revenue (in dollars) from the sale of x car seats for infants is given by the following function. r(x)=28x - 0.010x^2 0≤x≤2800 (a) find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (b) use the four - step process to find r(x). (c) find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (a) find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. 7.5 (round to one decimal place as needed.) (b) r(x)=□

Answer

Explanation:

Step1: Recall the power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the function $R(x)=28x - 0.010x^{2}$, we differentiate each term separately.

Step2: Differentiate the first term

For the term $y_1 = 28x$, where $a = 28$ and $n = 1$. Using the power - rule, $y_1^\prime=28\times1\times x^{1 - 1}=28$.

Step3: Differentiate the second term

For the term $y_2=-0.010x^{2}$, where $a=-0.010$ and $n = 2$. Using the power - rule, $y_2^\prime=-0.010\times2\times x^{2 - 1}=-0.02x$.

Step4: Find $R^\prime(x)$

By the sum - difference rule of differentiation $(u\pm v)^\prime = u^\prime\pm v^\prime$, we have $R^\prime(x)=y_1^\prime + y_2^\prime=28-0.02x$.

Answer:

$28 - 0.02x$