Intervals of Increase and Decrease for e^x = e^-2x

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    Calculus
In summary, the conversation discusses finding the intervals of increase and decrease for the equation y=e^x=e^-2x. The first derivative is taken and set equal to 0, but the question is how to solve for x. It is suggested to use logarithm properties and apply natural logarithm. The equation is simplified and the fraction is moved to the other side. The answer is found to be (ln2)/3.
  • #1
erik05
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Hello all. Really quick question here...What are the intervals of increase and decrease for y= e^x = e^-2x. I found the first derivative : y'= e^x-2e^-2x and set it equal to 0 but that's where I got stuck. How would you solve for x? I know that the answer is (ln2)/3 but how would you get there? Thanks.
 
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  • #2
Working out the equation, and use some logarithm properties.

Apply natural logaritm

[tex] (e^{x})^{3} = 2 [/tex]
 
  • #3
Stupid question...but why to the exponent of 3?
 
  • #4
[tex] 0= e^x-\frac{2}{e^{2x}} [/tex]

Just swing that fraction to the other side and multiply out.
 
  • #5
I can't believe I didn't get that...thanks.
 

FAQ: Intervals of Increase and Decrease for e^x = e^-2x

1. What is Calculus?

Calculus is a branch of mathematics that deals with the study of continuous change. It is used to analyze and understand complex phenomena, such as motion, growth, and change in physical quantities.

2. What is the difference between differential and integral calculus?

Differential calculus is concerned with the study of rates of change and slopes of curves, while integral calculus deals with the accumulation of quantities and finding the area under curves.

3. What is the fundamental theorem of calculus?

The fundamental theorem of calculus states that the process of finding the area under a curve can be reversed by finding the derivative of the function.

4. How is calculus used in real life?

Calculus is used in many fields, such as physics, engineering, economics, and statistics. It is used to model and solve problems involving rates of change and optimization.

5. Is calculus difficult to learn?

Calculus can be challenging to learn, but with patience and practice, it can be understood and applied effectively. It is important to have a strong foundation in algebra and trigonometry before learning calculus.

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