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sasho [114]
2 years ago
8

If dy/dx = x(y-1), find the equation of the tangent line at x=-2 with f(-2)=3

Mathematics
1 answer:
Lapatulllka [165]2 years ago
3 0

Answer:

The equation of the tangent line passing through the point (-2,3) is

 4 x + y +5 =0

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given that the slope of the tangent</em>

<em>              </em>m = \frac{dy}{dx} = x(y-1)<em></em>

<em>              m = -2( 3-1) = -4</em>

<em>Given point x = -2</em>

<em>          y = f(-2) =3</em>

<em>∴The given point ( x₁ , y₁) = ( -2 ,3)</em>

<u><em>Step(ii):-</em></u>

The equation of the tangent line passing through the point (-2,3)

y - y_{1} = m(x-x_{1} )

y -3 = -4(x-(-2))

y -3 = -4( x+2)

y-3 = -4x -8

4x + y -3+8=0

4x +y +5=0

<u><em>Step(iii):-</em></u>

<em>The equation of the tangent line passing through the point (-2,3) is</em>

<em>   4 x + y +5 =0</em>

<em></em>

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