find equations of the tangent line and normal line to the given curve at the specified point?? `Y=2xe^x` at the point (0,0) i can figure out tangent line but what is normal line??
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hala718
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The normal line is the line that is perpendicular to the tangent line.
First we will find the tangent line at the point (0,0).
f(x)= 2xe^x
==> The slope of the tangent line is the derivative at x= 0
==> f'(x)= (2x)'e^x + 2x(e^x)'
==> f'(x)= 2e^x + 2xe^x
==> f'(0) = 2e^0 + 2(0)e^0
==> f'(0) = 2
Then the slope of the tangent line is m= 2
==> y-y1 = m(x-x1)
==> y= 2x
Then, the tangent line is : `y= 2x`
`` Now we will find the slope of the normal line.
Since the normal line is perpendicular to the tangent line, then the slope is -1/2
==> y= (-1/2)x
Then, the normal line is :`y= -1/2 x`
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