determine the maximum and the minimum of the function on the interval given. f(x)=2^x; 2,5 min: max:

Explanation:

Step1: Analyze the function's monotonicity

The function $y = 2^{x}$ is an exponential - function with base $a = 2>1$, so it is an increasing function on the entire real - number line.

Step2: Find the minimum value

Since the function is increasing on $[2,5]$, the minimum value occurs at $x = 2$. Substitute $x = 2$ into $f(x)=2^{x}$, we get $f(2)=2^{2}=4$.

Step3: Find the maximum value

Since the function is increasing on $[2,5]$, the maximum value occurs at $x = 5$. Substitute $x = 5$ into $f(x)=2^{x}$, we get $f(5)=2^{5}=32$.

Answer:

min: 4 max: 32