anonymous
  • anonymous
Application of differentiation. Find the equation of the normal to the curve y=(x+2)e^x-3x at the point (0,2).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
dy/dx at (0,2) = 0 i don't know what to do next.
anonymous
  • anonymous
@ startanewww what did you get on your derivative at (0,2)?
anonymous
  • anonymous
isn't it 0?

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More answers

anonymous
  • anonymous
after getting the slope at (0,2) find the normal means perpendicular to the line at (0,2)
anonymous
  • anonymous
1st find the equation of tangent to the curve...
anonymous
  • anonymous
slope perpendicular to it is m2= - 1/m1
anonymous
  • anonymous
y-y1 = m(x-x1)
anonymous
  • anonymous
but the slope I found for dy/dx at (0,2) is zero. What can i do?
anonymous
  • anonymous
then, the slope of the normal will be -1/0 = infinity how can i find the equation of normal?
anonymous
  • anonymous
Diffrentiate y=(x+2)e^x-3x
anonymous
  • anonymous
u know Product Rule ?
anonymous
  • anonymous
u get slope = -1
anonymous
  • anonymous
SO...Slope of Normal = -1 / m1 = -1/-1 = 1
anonymous
  • anonymous
Nw just write the equation using points (0,2) m = 1 y-y1 = m(x-x1)
anonymous
  • anonymous
y'=e^x+(x+2)e^x-3 dy/dx at (0,2) = e^0 + (0+2)e^0 - 3 = 0
anonymous
  • anonymous
am i correct?
anonymous
  • anonymous
y=(x+2)e^x-3x y' = (x+2) *1 + e^x *1 - 3
anonymous
  • anonymous
differentiating e^x gives e^x right?
anonymous
  • anonymous
am i correct?
anonymous
  • anonymous
lets say y'=0, can you form a line perpendicular to the curve? try it :D
anonymous
  • anonymous
first fint an equation of the line tangent to the curve at (0,2)
anonymous
  • anonymous
(y-2)/(x-0)=0 y=2?
anonymous
  • anonymous
what about the equation of normal?
anonymous
  • anonymous
yes correct :D then ?
anonymous
  • anonymous
what can i do?
anonymous
  • anonymous
the slope will be infinity....
anonymous
  • anonymous
what is a line perpendicular to line y=2?
anonymous
  • anonymous
at (0,2) ?
anonymous
  • anonymous
will the slope of the normal be infinity ?
anonymous
  • anonymous
|dw:1356675309579:dw|
anonymous
  • anonymous
but -1/0 = infinity?
anonymous
  • anonymous
x=0 is the line
anonymous
  • anonymous
i don't know the answer....
anonymous
  • anonymous
i think you are right
anonymous
  • anonymous
ah ok theres no answer in the book? :D
anonymous
  • anonymous
my classmates said the answer was x=0
anonymous
  • anonymous
hmm the line perpendicular to y=2 is the y axis or the vertical line
anonymous
  • anonymous
ok so the answer should be x=0 only?
anonymous
  • anonymous
hmm it can be x=0
anonymous
  • anonymous
x = 0 to infinity?
anonymous
  • anonymous
it could be y= 0 to 2, or 2 to infinity, or y= 0 to negative infinity
anonymous
  • anonymous
?????? how come
anonymous
  • anonymous
equation of the normal at (0,2)...? should there be only one answer?
anonymous
  • anonymous
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 ________ ?
anonymous
  • anonymous
vertical lines
anonymous
  • anonymous
?
anonymous
  • anonymous
the vertical line y axis
anonymous
  • anonymous
yess correct :D
anonymous
  • anonymous
so what is the final answer? x=0 ?
anonymous
  • anonymous
i would say at point (0,2) it is y= from 0 to 2 vertical line
anonymous
  • anonymous
ok thanks
anonymous
  • anonymous
ok YW,,, good luck now :D

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