analyze the minimum and maximum value of the function f(x)=e^x on the given interval -1,4 the minimum value…

analyze the minimum and maximum value of the function f(x)=e^x on the given interval -1,4 the minimum value of f(x)=e^x on -1,4 is 0.368 (type an integer or decimal rounded to the nearest thousandth as needed.) the maximum value of f(x)=e^x on -1,4 is (type an integer or decimal rounded to the nearest thousandth as needed.)

analyze the minimum and maximum value of the function f(x)=e^x on the given interval -1,4 the minimum value of f(x)=e^x on -1,4 is 0.368 (type an integer or decimal rounded to the nearest thousandth as needed.) the maximum value of f(x)=e^x on -1,4 is (type an integer or decimal rounded to the nearest thousandth as needed.)

Answer

Explanation:

Step1: Analyze the derivative

The derivative of $f(x)=e^{x}$ is $f^\prime(x)=e^{x}$. Since $e^{x}>0$ for all real - numbers $x$, the function $y = e^{x}$ is increasing on the entire real - line.

Step2: Evaluate at endpoints

For the interval $[-1,4]$, we evaluate the function at the endpoints. When $x=-1$, $f(-1)=e^{-1}=\frac{1}{e}\approx0.368$. When $x = 4$, $f(4)=e^{4}$. Calculate $e^{4}\approx54.598$.

Answer:

54.598