Which of the following is a point at which the tangent to y = -xe^(2x) is horizontal?
The answer is (-0.5,0.18) where did the 0.18 come from?

Question

Which of the following is a point at which the tangent to y = -xe^(2x)  is horizontal?
The answer is (-0.5,0.18) where did the 0.18 come from?

anonymous · Answer

when u draw the graph u get y value 0.18

zale101 · Answer

When you take the derivative of y = -xe^(2x) 
$y'=-2xe^{2x}-e^{2x}$
you set it equal to zero
$y'=-2xe^{2x}-e^{2x}=$$-e^{2x}(2x+1)$
x= -0.5
Now, we have the x value of the tangent line, plug that back to the original equation

zale101 · Answer

y = -xe^(2x) 
plug (-0.5)
y=-(-0.5)e^(2(-0.5))
y=0.18...

anonymous · Answer

Oh! thank you so much, both of you

anonymous · Answer

try wolfram alpha to see the graph so u know for sure

zale101 · Answer

You're welcome

anonymous · Answer

you will see something like this , it really helps when u can see it !