Chapter 1.8, Problem 3GP

To determine

To estimate and interpret: The region where the function graphed in Guided Practice $1$ is positive, negative, increasing, or decreasing, the $x-\text{coordinate}$ of any relative extrema and the end behavior of the graph.

Answer to Problem 3GP

The given function is positive when $x>1$ , negative when $x<1$ , increasing for all given values of $x$ , has no relative extrema and the end behavior of the graph indicates after $5hours$ , temperature is the highest, i.e., $20°C$ .

Explanation of Solution

Given information: A graph showing the temperature $y$ of a medical sample thawed at a controlled rate is given.

Positive: The given function is positive where the graph lies above the $x-axis$ , i.e., where the temperature is greater than $0°C$ , i.e. when $x>1$ .

Negative: The given function is negative where the graph lies below the $x-axis$ , i.e., where the temperature is less than $0°C$ , i.e. when $x<1$ .

Increasing/Decreasing: The given function is increasing where the graph goes up. Now, when time increases, then temperature also increases. So the graph is increasing for all given values of $x$ .

Relative extrema: As there are no points of relatively high or low function values, so the given function has no relative extrema.

End behavior: The end behavior of the graph indicates that as time passes, the temperature gets higher and higher (or the day gets warmer and warmer) and after $5\text{hours}$ , it is the highest, i.e., $20°C$ .