Tangent Lines and Equations

Question

Your job is to find the equation of a tangent line to the curve at the point (1,2)

x^4+xy+y^2=7 step by step

Answer 1

the process for tangent lines think of y as f(x), then you get the equation

x^4+x*f(x)+f(x)^2=7

No differentiate with respect to x

4x^3+x*df/dx+f(x)+2*f(x)*df/dx=0

or in terms of y

4x^3+x*dy/dx+y+2*y*dy/dx=0

Substitute the x and y values you know. x=1 y=2. Then solve for dy/dx. This is the slope of the tangent line