Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + y2 = (4x2 + 2y2 − x)2
(0, 0.5)
(cardioid)

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

Step 3: Find dy/dx at the point (0, 0.5)

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2