Find an equation of the tangent line to the curve at the given point.

Question

y = x^3 -3x +1   (2,3)

Answer 1

Step 1:

The equation of the curve is .

Apply derivative on each side with respect to .

Substitute in above equation.

This is the slope of tangent to the curve at a point .

.

Step 2:

Find the tangent line using the point slope form : .

Where is the slope.

Substitute the values and in point slope form.

Solution :

The tangent line equation is .