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Application of differentiation.
Find the equation of the normal to the curve y=(x+2)e^x3x at the point (0,2).



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dy/dx at (0,2) = 0
i don't know what to do next.

mark_o.
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@ startanewww what did you get on your derivative at (0,2)?

startanewww
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isn't it 0?

mark_o.
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after getting the slope at (0,2) find the normal means perpendicular to the line at (0,2)

Yahoo!
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1st find the equation of tangent to the curve...

mark_o.
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slope perpendicular to it is m2=  1/m1

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yy1 = m(xx1)

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but the slope I found for dy/dx at (0,2) is zero. What can i do?

startanewww
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then, the slope of the normal will be 1/0 = infinity
how can i find the equation of normal?

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Diffrentiate y=(x+2)e^x3x

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u know Product Rule ?

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u get slope = 1

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SO...Slope of Normal = 1 / m1 = 1/1 = 1

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Nw just write the equation using points (0,2) m = 1
yy1 = m(xx1)

startanewww
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y'=e^x+(x+2)e^x3
dy/dx at (0,2) = e^0 + (0+2)e^0  3 = 0

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am i correct?

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y=(x+2)e^x3x
y' = (x+2) *1 + e^x *1  3

startanewww
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differentiating e^x gives e^x right?

startanewww
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am i correct?

mark_o.
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lets say y'=0, can you form a line perpendicular to the curve? try it :D

mark_o.
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first fint an equation of the line tangent to the curve at (0,2)

startanewww
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(y2)/(x0)=0
y=2?

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what about the equation of normal?

mark_o.
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yes correct :D then ?

startanewww
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what can i do?

startanewww
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the slope will be infinity....

mark_o.
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what is a line perpendicular to line y=2?

mark_o.
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at (0,2) ?

startanewww
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will the slope of the normal be infinity ?

mark_o.
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dw:1356675309579:dw

startanewww
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but 1/0 = infinity?

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x=0 is the line

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i don't know the answer....

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i think you are right

mark_o.
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ah ok theres no answer in the book? :D

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my classmates said the answer was x=0

mark_o.
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hmm the line perpendicular to y=2 is the y axis or the vertical line

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ok so the answer should be x=0 only?

mark_o.
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hmm it can be x=0

startanewww
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x = 0 to infinity?

mark_o.
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it could be y= 0 to 2, or 2 to infinity, or y= 0 to negative infinity

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?????? how come

startanewww
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equation of the normal at (0,2)...? should there be only one answer?

mark_o.
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because line tangent to the curve is y=2 or the horizontal line, now the line normal to it is the line perpendicular to y=2,, w/c are ________ ?

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vertical lines

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?

mark_o.
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the vertical line y axis

mark_o.
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yess correct :D

startanewww
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so what is the final answer? x=0 ?

mark_o.
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i would say at point (0,2) it is y= from 0 to 2 vertical line

startanewww
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ok thanks

mark_o.
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ok YW,,, good luck now :D