Sure! Let's find the simplified form of the function [tex]\( f(x) = (2e^x) \cdot (3x^2) \)[/tex].
To determine the simplified expression, we'll follow the steps below:
1. Identify the given expression:
[tex]\[
f(x) = (2e^x) \cdot (3x^2)
\][/tex]
2. Combine the constants:
Notice that the constants 2 and 3 can be multiplied together:
[tex]\[
2 \cdot 3 = 6
\][/tex]
3. Rewrite the expression with the combined constants:
Substitute [tex]\(6\)[/tex] for the constants combination:
[tex]\[
f(x) = 6 \cdot e^x \cdot x^2
\][/tex]
4. Write the simplified expression clearly:
[tex]\[
f(x) = 6x^2e^x
\][/tex]
So, the simplified form of the function [tex]\( f(x) \)[/tex] is:
[tex]\[
f(x) = 6x^2e^x
\][/tex]
That's the final answer.
