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

1 Answer
Nov 17, 2017

Answer:

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#