A company estimates that it will sell (x) units of a product after spending x thousand dollars on advertising, as given by (x)=−5x3+235x2−3400x+20000,10≤x≤40. (A) Use interval notation to indicate when the rate of change of sales ′(x) is increasing. Note: When using interval notation in WeBWorK, remember that: You use 'I' for [infinity] and '-I' for −[infinity], and 'U' for the union symbol. If you have extra boxes, fill each in with an 'x'. ′(x) increasing:

The rate of change is how much the company sales changes after spending

The rate of change increases at: (10, 20)

The function is given as:

Differentiate, to calculate the rate of change

Set to 0

Divide through by 5

Using a calculator, we have:

The domain is given as:

When x = 10, we have:

When x = 11.3, we have:

When x = 20, we have:

When x = 40, we have:

The value of f'(x) increases at x = 10 to 20.

Hence, the rate of change increases at: (10, 20)

Read more about rates at:

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Step-by-step explanation:

If the Number of Sales of x units, N(x) is defined by the function:

Next, we text the critical points and the end points of the interval to see where the derivative is increasing.

Thus, the rate of change of sales is increasing in the interval on 10≤x≤40.

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