Engineering Board Exam Reviewer · Tangent and Normal Lines · hard

Find the equation of the tangent line to x2+xy+y2=7 at the point (2,1).

  1. 5x-4y=6
  2. 4x+5y=13
  3. 5x+4y=11
  4. 5x+4y=14

Answer

D. 5x+4y=14

Solution

Differentiate: 2x+y+xy'+2yy'=0 y'=-2x+y/x+2y. At (2,1): y'=- 54. The tangent is y-1=- 54(x-2) 5x+4y=14.

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  4. Find the equation of the normal line to y= x at x=4.
  5. Find the equation of the tangent line to y=x2 at the point (3,9).
  6. Find the slope of the tangent line to y=x3-2x at x=2.
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