Write the equation of the tangent line to the graph of the function y = x ^ 3-3x ^ 2

We have a function:

y = x ^ 3 – 3 * x ^ 2.

Let’s write down its tangent equation.

The tangent equation is usually written to the graph of the function at a certain point, which has enough abscissa to fully formulate the equation of the line. Let’s write the equation in general form:

y = y ‘(x0) * (x – x0) + y (x0);

Find the derivative of the function:

y ‘(x) = 3 * x ^ 2 – 6 * x.

Then our equation will take the following form:

y = (3 * x0 ^ 2 – 6 * x0) * (x – x0) + x0 ^ 3 – 3 * x0 ^ 2.

Substitute for x0 the value of the abscissa of the point and find the definite equation of the line.