Tangent line at the Curve

Question

Find the tangent line to the curve 3x²+6y² = 1 at x = 1/2

Answer 1

3x² + 6y² = 1

Solve this equation for y, and evaluate y at x=1/2. That will give you the y-coordinate of the tangent point. Let (1/2,y₀) be the tangent point, where y₀ is y evaluated at x=1/2.

Get y' from implicit differentiation.

6x + 12yy' = 0

At the tangent point,

6(1/2) + 12y₀y' = 0

Solve this equation for y'. That gives the slope of the tangent line. Call it m.

m = y'(1/2,y₀)

Equation of tangent line:

y = mx + b

Find b from the point (1/2,y₀).

y₀ = m(1/2) + b

You have all the steps you need to solve the problem; it is a matter of doing the math. You take it from here.