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Given the function [tex]f(x) = 6e^x[/tex], evaluate each of the following. Round your answers to two decimal places as needed.

1. [tex]f(-3) =[/tex] [tex]\square[/tex]
2. [tex]f(-1) =[/tex] [tex]\square[/tex]
3. [tex]f(0) =[/tex] [tex]\square[/tex]
4. [tex]f(1) =[/tex] [tex]\square[/tex]
5. [tex]f(3) =[/tex] [tex]\square[/tex]


Sagot :

Let's evaluate the function [tex]\( f(x) = 6 e^x \)[/tex] at the specified points. We'll calculate [tex]\( f(-3) \)[/tex], [tex]\( f(-1) \)[/tex], [tex]\( f(0) \)[/tex], [tex]\( f(1) \)[/tex], and [tex]\( f(3) \)[/tex] and round the results to two decimal places.

1. Evaluate [tex]\( f(-3) \)[/tex]:
[tex]\[ f(-3) = 6 e^{-3} \][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[ f(-3) \approx 0.30 \][/tex]

2. Evaluate [tex]\( f(-1) \)[/tex]:
[tex]\[ f(-1) = 6 e^{-1} \][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[ f(-1) \approx 2.21 \][/tex]

3. Evaluate [tex]\( f(0) \)[/tex]:
[tex]\[ f(0) = 6 e^{0} \][/tex]
Since [tex]\( e^0 = 1 \)[/tex], we have:
[tex]\[ f(0) = 6 \cdot 1 = 6.00 \][/tex]

4. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[ f(1) = 6 e^{1} \][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[ f(1) \approx 16.31 \][/tex]

5. Evaluate [tex]\( f(3) \)[/tex]:
[tex]\[ f(3) = 6 e^{3} \][/tex]
After calculating the value and rounding to two decimal places, we get:
[tex]\[ f(3) \approx 120.51 \][/tex]

The evaluated values of the function at the given points are:
[tex]\[ \begin{align*} f(-3) & \approx 0.30, \\ f(-1) & \approx 2.21, \\ f(0) & = 6.00, \\ f(1) & \approx 16.31, \\ f(3) & \approx 120.51. \end{align*} \][/tex]