Rate of Change of Body Temperature During Illness Calculus Problem

Published on September 17, 2026

Calculus

Learn how to find the rate of change of body temperature over time by applying the quotient rule for derivatives to a rational function modeling an illness.

Question

Answer

Given the temperature function:

(a) Find the rate of change of the temperature with respect to time.

To find the rate of change, we calculate the derivative

using the quotient rule

:
Let

and

(b) Find the temperature at hr.

Substitute

into the original function

© Find the rate of change of the temperature at hr.

Substitute

into the derivative

found in part (a):

Final Answers:
(a)

(b)

(or

)
©

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