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How to solve this? please help me

How to solve this? please help me-example-1

1 Answer

5 votes

Answer:

  • tangent: y = 2x -2
  • normal: y = -1/2x +3

Explanation:

Differentiating implicitly, you have ...

-y²·dx +(4-x)(2y)dy = 3x²·dx

So, the slope is ...

dy/dx = (3x² +y²)/(2y(4 -x))

At (x, y) = (2, 2), the slope of the curve is ...

dy/dx = (3·2² +2²)/(2·2(4 -2)) = 16/8 = 2

In point-slope form, the equation of the tangent line is then ...

y = m(x -h) +k

y = 2(x -2) +2

y = 2x -2 . . . . equation of tangent line

__

The normal to the curve is perpendicular to the tangent at the same point. The slope of the perpendicular line is the negative reciprocal of the tangent's slope, so is -1/2.

y = (-1/2)(x -2) +2

y = -1/2x +3 . . . equation of normal line

How to solve this? please help me-example-1
User Xavier Lamorlette
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