The steps of finding the tangent equation of a function image passing through a certain point are as follows:

(1) Let the tangent point be (x0, y0);

(2) Find the derivative function of the original function, and substitute x0 into the derivative function to get the slope k of the tangent;

(3) The tangent equation is written from the slope k and the tangent point (x0, y0) by using the point inclination equation of the straight line;

(4) Substitute the fixed-point coordinates into the tangent equation to get the equation 1, and substitute the tangent point (x0, y0) into the original equation.

Extended data

Example:

Find the tangent equation of curve y = x at (-1, 3) -2x. ?

Solve the problem:

The title "at" (-1,3) means that the coordinates must be on the curve.

y = x？ -2 times

y' = 2x - 2

Tangent slope = y' | (x =-1) = 2 (-1)-2 =-4.

So the tangent equation is y-3 = -4(x+ 1).

That is 4x+y+ 1 = 0.

So the answer is 4x+y+ 1 = 0.