# How do you find the maximum value of f(x)=20e^(-2x)*sin(3x) ?

Nov 17, 2017

The maximum value of $f \left(x\right)$ is infinity.

#### Explanation:

Let $f \left(x\right) = 20 {e}^{- 2 x} \sin 3 x$.

In order to find the maximum value of $f \left(x\right)$, we need to consider the functions which make up $f$ and their maximum values. $f$ is a product of $3$ functions: $20$, ${e}^{- 2 x}$ and $\sin 3 x$. So the maximum of $f$ will be the product of the maximum of these three functions.

• The max value of $20$ is $20$.
• The max value of ${e}^{- 2 x}$ is $\infty$
• The max value of $\sin 3 x$ is $1$

It is also important to note that all three of these functions can take their max values simultaneously.

So the max value of $f$ is $20 \cdot \infty \cdot 1 = \infty$