Find the equation of the tangent line to the parabola y = x ^ 2 -3x-1 at the point x zero = 3.

In order to write the equation of the tangent to the parabola, we recall that the tangent of the angle of inclination of the tangent is equal to the derivative of a given function.

y = x ^ 2 – 3x – 1;

We are looking for a derivative:

y ‘= 2x – 3.

So, the point at which the tangent is drawn has coordinates (3; y0).

Find the ordinate, it is equal to y0 = 3 ^ 2 – 3 * 3 – 1 = 9 – 9 – 1 and then the coordinates of the point are (3; -1).

The tangent equation has the form y = y ‘* x + b, where

y ‘= 2 * 3 – 3 = 6 – 3 = 3;

-1 = 3 * 3 + b and b = -10.

Let’s write the equation of the tangent line: y = 3x – 10.

Answer: y = 3x – 10.