Can someone help me with the answer?

Question

Help me pleasee

k = 4.61

Find the equation of the normal line of the curve f (x, y) at the point y = 0.5

f(x, y): 4y3 - kx = cos(y5 - y3)​

Answer 1

I will not do the numerical work for you, but I will tell you how to proceed.

Use implicit differentiation to find dy/dx.

Find the value of x when y=.5 (substitute in the equation for f(x,y) and solve for x).

Evaluate dy/dx at the point you have just found.

This is the slope of the tangent to f(x,y) at the point in question.

The slope of the normal is the negative reciprocal of the slope of tangent line.

Now use the point-slope equation to write the equation of the normal line.