Find the equation of the curve passing through the point A (-2; 3) if the tangent of the curve at each point is 3x

Let us write the equation of the tangent to the graph of the function at a point with abscissa m0:

y = f ‘(m0) * (m – m0) + y (m0);

The tangent at any point to the graph of the function is 3 * m.

With a variable in the tangent equation, the value of the derivative of the function at the point m0 is found:

f ‘(m0) = 3;

Then we get:

f (m) = 3 * m + C, where C is const.

Now we substitute the values of the coordinates of the point belonging to the graph of the function:

3 = 3 * (-2) + C;

C = 9;

y = 3 * m + 9 are the equations of our function.