Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

m.auld64

  • 4 years ago

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

  • This Question is Closed
  1. experimentX
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  2. experimentX
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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

  3. experimentX
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is that log base 2??

  4. No-data
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes it is.

  5. No-data
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I got this: \[(\ln 3)3^x+\frac{1}{(\ln 2)xy}\left(x\frac{dy}{dx}+y\right)=0\]

  6. No-data
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you can solve for \[\frac{dy}{dx}\] and substitute the coordinates given. so you'll have the slope.

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy