For $11 \leq t \leq 25$, the cooling process of the mixture can be approximated by the function $u _ { 2 }$ defined on $\mathbb { R }$ with $u _ { 2 } ( t ) = 18 + 36 \cdot \mathrm { e } ^ { - 0,033 \cdot t }$. Here, $t$ again denotes the time in minutes since the beginning of the investigation and $u _ { 2 } ( t )$ denotes the temperature of the mixture in ${ } ^ { \circ } \mathrm { C }$. The graph of $u _ { 2 }$ is monotonically decreasing. Determine the average rate of change of the temperature of the coffee in the first 10 minutes of the investigation and the average rate of change of the temperature of the mixture from the 11th to the 21st minute of the investigation. Compare the results.
For $11 \leq t \leq 25$, the cooling process of the mixture can be approximated by the function $u _ { 2 }$ defined on $\mathbb { R }$ with $u _ { 2 } ( t ) = 18 + 36 \cdot \mathrm { e } ^ { - 0,033 \cdot t }$.
Here, $t$ again denotes the time in minutes since the beginning of the investigation and $u _ { 2 } ( t )$ denotes the temperature of the mixture in ${ } ^ { \circ } \mathrm { C }$. The graph of $u _ { 2 }$ is monotonically decreasing.
Determine the average rate of change of the temperature of the coffee in the first 10 minutes of the investigation and the average rate of change of the temperature of the mixture from the 11th to the 21st minute of the investigation.
Compare the results.