8.0k views
1 vote
Write the equation of lines tangent and normal to the following function at x derivative, use implicit differentiation.

1. To find x2y + yx = 2x

User Pejalo
by
8.1k points

1 Answer

4 votes

Final answer:

To find the equation of the lines tangent and normal to the function x^2y + yx = 2x using implicit differentiation, we need to find the first derivative of the equation and substitute a given point to get the equations of the tangent and normal lines.

Step-by-step explanation:

To find the equation of the lines tangent and normal to the function x^2y + yx = 2x using implicit differentiation, we need to find the first derivative of the equation. Differentiating both sides with respect to x, we get 2xy + x^2(dy/dx) + y = 2. Solving for dy/dx, we get dy/dx = (2 - 2xy)/(x^2 + 1).

To find the equation of the tangent line, we substitute the given point (x₀, y₀) into the equation dy/dx. Then, we use the point-slope form y - y₀ = m(x - x₀), where m is the slope dy/dx. This gives us the equation of the tangent line. To find the equation of the normal line, we use the fact that the slope of a normal line is the negative reciprocal of the slope of the tangent line. So, the equation of the normal line can be obtained using the same point-slope form but with the negative reciprocal slope.

User David Specht
by
8.8k points

Related questions

asked Aug 26, 2023 207k views
Eblume asked Aug 26, 2023
by Eblume
6.9k points
1 answer
3 votes
207k views
asked Oct 4, 2023 41.2k views
Bday asked Oct 4, 2023
by Bday
9.2k points
1 answer
3 votes
41.2k views