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 . (type an integer or decimal rounded to the nearest thousandth as needed.)
Answer
Explanation:
Step1: Find the derivative
The derivative of $f(x)=e^{x}$ is $f^\prime(x)=e^{x}$. Since $e^{x}>0$ for all real - valued $x$, the function $y = e^{x}$ is always increasing.
Step2: Evaluate the function at endpoints
Evaluate $f(x)$ at the endpoints of the interval $[-1,4]$. When $x=-1$, $f(-1)=e^{-1}=\frac{1}{e}\approx0.368$. When $x = 4$, $f(4)=e^{4}\approx54.598$.
Answer:
$0.368$