(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f be the function given by f(x) = 3e^2x and let g be the function given by g(x) = 6x^3. At what value of x do the graphs of f and g have parallel tangent lines?

a. -0.701

b. -0.567

c. -0.391

d. -0.302

e. -0.258

Correct answer is c. -0.391

2. Relevant equations

3. The attempt at a solution

Well, tangent line means doing the derivative. Thus, I did the derivative of f and g.

f'(x) = 6e^2x

g'(x) = 18x^2

Parallel means the slopes or the derivatives are the same. Thus, I set them equal to each other in order to solve for x.

f'(x) = g'(x)

6e^2x = 18x^2

e^2x = 3x^2

Here I was stuck. I could do ln(e^2x) to cancel out the e, but I would end up with something ugly on the right side.

2x = ln(3x^2)

and I wouldn't have x on one side. Am I approaching this problem incorrectly, or is my algebra wrong?

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# Homework Help: What value of x do the graphs of f and g have parallel tangent lines?

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