Question

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

Answer 1

The maximum value of `f(x)` is infinity.

Explanation:

Let `f(x)=20e^(-2x)sin3x`.

In order to find the maximum value of `f(x)`, we need to consider the functions which make up `f` and their maximum values. `f` is a product of `3` functions: `20`, `e^(-2x)` and `sin3x`. 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^(-2x)` is `oo`
• The max value of `sin3x` 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*oo*1=oo`