Question

If normal to the curve y=f(x) is parallel to x- axis then dy/dx =0 or dx/dy =0

Answer 1

Proved

•y=f(x)

•slope of tangent = tanθ = dy/dx

•slope of normal = tanθ = -dx/dy

•Note: tanθ is slope of tangent and normal are not same

• θ is the angle b/w Xaxis and the line whose slope is to be calculated

•As, Normal is parallel to X axis

•Here, θ = 0 so tanθ = 0

•slope =0

•-dx/dy = 0

•hence proved