The temperature of a person during an intestinal illness is given by $$T(t)=-0.1 t^{2}+1.2 t+98.6, \quad 0 \leq t \leq 12$$ where $T$ is the temperature $\left({ }^{\circ} \mathrm{F}\right)$ at $t$ days. Find the relative extrema and sketch a graph of the function.
Added by Hector R.
Step 1
Given that $a = -0.1$ and $b = 1.2$, we have: $t = -\frac{1.2}{2(-0.1)} = 6$ days. ** Show more…
Show all steps
Close
Your feedback will help us improve your experience
Vishal Parmar and 57 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The temperature of a person during an intestinal illness is modeled by T(t) = -0.1t^2 + 1.2t + 98.6, where T is the temperature after t days and 0 ≤ t ≤ 12. Find the largest and smallest values of the temperature during the given time period.
Kathleen C.
Temperature During an Illness. The temperature of a patient during an illness is given by the function $$T(t)=-0.1 t^{2}+1.2 t+98.6, \quad 0 \leq t \leq 12$$ where $T$ is the temperature, in degrees Fahrenheit, at time $t,$ in days, after the onset of the illness. A. Graph the function using a graphing calculator. B. Use the MAXIMUM feature to determine at what time the patient's temperature was the highest. What was the highest temperature?
More on Functions
Increasing, Decreasing, and Piecewise Functions; Applications
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 $12 .$
Differentiation
Rates of Change: Velocity and Marginals
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD