Question

Find the equation of the normal line of the curve f (x, y) at the point y = 0.5
`f(xy)4y3−kx=cos(y5−y3)`​

Answer 1

To find the equation of the normal line of a curve at a given point, differentiate the equation of the curve, find the slope of the tangent line, and then find the negative reciprocal of that slope.

Step-by-step explanation:

To find the equation of the normal line of a curve at a given point, we need to find the derivative of the curve at that point, and then find the negative reciprocal of the derivative to get the slope of the normal line. First, we need to differentiate the equation of the curve with respect to x. After finding the derivative, plug in the x-coordinate of the given point to find the slope of the tangent line. The negative reciprocal of this slope will give us the slope of the normal line. Finally, use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the normal line, to find the equation of the normal line.