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??
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).
==> 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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