Goten77
  • Goten77
y=xe^(-x/8) y1=x(e^(-x/8))(-1/8) + e^(-x/8)(1) critical points ima type this below along w/ the question
Mathematics
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jamiebookeater
  • jamiebookeater
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Goten77
  • Goten77
\[y=xe ^{-x/8}\] then derivative is this correct? \[y ^{1}=xe ^{-x/8}(-1/8) + e ^{-x/8}1\]
campbell_st
  • campbell_st
simplifying your 1st derivative you will have \[\frac{dy}{dx} = e^{-\frac{x}{8}}(-\frac{1}{8} x + 1)\] so you need to solve \[-\frac{1}{8} x + 1 = 0\]
Goten77
  • Goten77
ok thats what i got and then i get like -1/8x = -1 then x=-1/(-1/8) = +8

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campbell_st
  • campbell_st
thats correct.... that is the only value of x that makes the 1st derivative = 0...
Goten77
  • Goten77
oh nvm i c y e^o=1 eh i aint thinking
campbell_st
  • campbell_st
if you have x = 0 then \[dy/dx = e^{-\frac{0}{8}}(-\frac{1}{8}\times 0 + 1) = 1\] because \[e^{\frac{0}{8}} = 1\] any number to a power of zero is 1 so only 1 critical point...
Goten77
  • Goten77
man i made so many simple mistakes on this last quiz... today i just aint thinking... oh well atleast i got this concept right XD

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