If a person's temperature after x hours of strenuous exercise is t(x) = x3(8 − x2) + 98.6 degrees fahrenheit (for 0 ≤ x ≤ 2), find the rate of change of the temperature after 1 hour.

Given function :

Soltution: Distributing x^3 over (8-x^2), we get 8x^3 -x^5.

Therefore,

Finding first derivative of the above function, because first derivative represents the rate of change.

We need to find rate of change of the temperature after 1 hour.

So, we need to plug x=1 in first derivarive of the function.

Therefore, after 1 hour, the person's temprature is increasing by 19° per hour.

The rate of change of the temperature after 1 hour is 19 degrees Fahrenheit per hour.

Given

If a person's temperature after x hours of strenuous exercise is t(x) = x3(8 − x2) + 98.6 degrees Fahrenheit (for 0 ≤ x ≤ 2).

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.

The given function is;

To find the rate of change of the given function differentiates the function with respect to x.

Therefore,

The rate of change after one hour is;

Hence, the rate of change of the temperature after 1 hour is 19 degrees Fahrenheit per hour.

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