Question
Use the Product Rule to find \( f(1) \) given that \( f(x)=2 x^{5} e^{x} \) \( f(1)=\square \) (Type an exact answer.)
Ask by Wells Pope. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(1) = 2e \)
Solution
1. Recognize that the function is given by
\[
f(x)=2x^5e^x.
\]
2. To find \( f(1) \), substitute \( x=1 \) into the function:
\[
f(1)=2(1)^5e^1.
\]
3. Simplify the expression:
\[
f(1)=2\cdot 1 \cdot e = 2e.
\]
Thus, the exact answer is
\[
\boxed{2e}.
\]
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Simplify this solution The Deep Dive
To find \( f(1) \) for the function \( f(x) = 2x^5 e^x \), we first plug \( x = 1 \) into the function: \[ f(1) = 2(1)^5 e^{1} = 2 \cdot 1 \cdot e = 2e. \] Thus, the exact answer is: \[ f(1) = 2e. \]
