At noon a child's temperature is 101° and is rising at an increasing rate. At 1 pm the child is given Tylenol. After 2 pm, the temperature is still increasing, but at a decreasing rate. The temperature reaches a peak of 103° at 3 pm and decreases to 100° by 5 pm.
Draw a graph that would represent this situation.

Here is the graph representing the temperature change of the child from noon to 5 PM. It shows the temperature rising sharply between noon and 2 PM, peaking at 3 PM, and then gradually decreasing to 100°F by 5 PM.

Would you like any details about the graph, or do you have any questions?

Here are 5 related questions:
1. How could we mathematically model the temperature rise and fall using a function?
2. What other factors might affect the rate of temperature change in this scenario?
3. Could this graph represent other physical processes? Why or why not?
4. How could medication like Tylenol affect the temperature model?
5. What would the graph look like if the child’s temperature had stabilized after 2 PM?

**Tip:** When drawing graphs for real-life situations, it's important to capture key turning points, like peaks and when rates change.

At noon a child's temperature is 101° and is rising at an increasing rate. At 1 pm the child is given Tylenol. After 2 pm, the temperature is still increasing, but at a decreasing rate. The temperature reaches a peak of 103° at 3 pm and decreases to 100° by 5 pm. Draw a graph that would represent this situation.

This problem demonstrates the graphical representation of a child's temperature change over time, involving increasing and decreasing rates of change. It covers key calculus concepts, including inflection points and the first/second derivative tests. Suitable for students in Grades 10-12.

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