Timothy Behan, Mathematics Teacher at Horace Mann School, Numerade Educator

09:04

Calculus an Applied Approach

Health The temperature $T$ (in degrees Fahrenheit) of a person during an illness can be modeled by the equation $T=-0.0375 t^{2}+0.3 t+100.4,$ where $t$ is time in hours since the person started to show signs of a fever.
(a) Use a graphing utility to graph the function. Be sure to choose an appropriate window.
(b) Do the slopes of the tangent lines appear to be positive or negative? What does this tell you?
(c) Evaluate the function for $t=0,4,8,$ and $12 .$
(d) Find $d T / d t$ and explain its meaning in this situation.
(e) Evaluate $d T / d t$ for $t=0,4,8,$ and $12 .$

Chapter 2: Differentiation

Section 3: Rates of Change: Velocity and Marginals