anonymous
  • anonymous
use implicit differentiation to find the slope of the tangent line to the curve 3^x + log_2(xy) = 10 at the point (2,1) and use it to find the equation of the tangent line in the form y = mx + b
Mathematics
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katieb
  • katieb
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experimentX
  • experimentX
differentiate it and get the differential equation 3^x*ln(3) + 1/(xy)*{1+xdy/dx} = 0 find value of dy/dx which is .. roughly -21 http://www.wolframalpha.com/input/?i=3%5E2*ln%283%29+%2B+1%2F2%281%2Bx%29+%3D+0 which is the slope of the tangent, since you know slope m, and you have point (2,1) find the value of b, you have your tangent
experimentX
  • experimentX
oops sorry, slope is around -1.05 http://www.wolframalpha.com/input/?i=3%5E2*ln%283%29+%2B+1%2F%282%281%2Bx%29%29+%3D+0
experimentX
  • experimentX
is that log base 2??

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anonymous
  • anonymous
yes it is.
anonymous
  • anonymous
I got this: \[(\ln 3)3^x+\frac{1}{(\ln 2)xy}\left(x\frac{dy}{dx}+y\right)=0\]
anonymous
  • anonymous
you can solve for \[\frac{dy}{dx}\] and substitute the coordinates given. so you'll have the slope.

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