SOLUTION: The curve y = e^x + 4e^-2x has one stationary point. Find the x-coordinate of this point

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Question 883678: The curve y = e^x + 4e^-2x has one stationary point.
Find the x-coordinate of this point
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We find the stationary point by finding dy/dx and setting the result to 0 and solving for x
note that dy/dx of e^x is e^x and dy/dx of e^-2x is e^-2x, therefore
dy/dx of e^x + 4e^-2x is e^x -8e^-2x
now let's set it = 0
e^x -8e^-2x = 0 then
e*x = 8/e^2x
multiply both sides of = by e^2x
e^3x = 8
use definition of logarithms
3x = ln 8
3x = 2.07944154
x = 0.69314718
this is the x co-ordinate of the stationary point