Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 y2 = (3x2 2y2 − x)2 (0, 0.5) (cardioid)

The equation of tangent is y=x+0.5

Step-by-step explanation:

Given:

We need to find the equation of tangent on curve at (0,0.5)

First we find slope of tangent using differentiation at given point.

Differentiate both side w.r.t x

Put x=0 and y=0.5 to solve for y'

Derivative at given point is slope of tangent line.

Thus, Slope = 1 and point: (0,0.5)

Using point slope form to find the equation of tangent line.

Hence, The equation of tangent is y=x+0.5

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w