From the tangency of the two functions, we can know that the two functions have a little commonality * * * and the slope of this point is equal, and (x, y) is equal, so we can take the derivative. If we solve the two solutions together with the simultaneous function group, we can get the undetermined coefficient.

If a straight line intersects a curve at two points, and the two points are infinitely close and tend to overlap, then the straight line is the tangent of the curve at that point. In junior high school mathematics, if a straight line is perpendicular to the radius of a circle and passes through the outer end of the radius of the circle, it is said that the straight line is tangent to the circle. Tangency is the positional relationship between a circle on a plane and another geometric shape.

Here, when "another geometry" is a circle or a straight line, there is only one intersection point (common point) between them, and when "another geometry" is a triangle, there is only one intersection point between each side of the circle and the triangle. This intersection is the tangent point.

Extended data:

Slope indicates the inclination of a straight line (or tangent of a curve) with respect to a (horizontal) coordinate axis. It is usually expressed by the tangent of the angle between a straight line (or the tangent of a curve) and a (horizontal) coordinate axis, or the ratio of the difference between the ordinate and abscissa of two points.

When the slope of the straight line L exists, the oblique formula y=kx+b, and when x=0, Y = B. ..

When the slope of the straight line L exists, is the point oblique?

=k().

For any point on any function, its slope is equal to the angle formed by its tangent and the positive direction of X axis, that is, k=tanα.

Slope calculation: ax+by+c=0, where k=.

The product of slopes of two vertically intersecting lines is-1: =- 1.

The slope of a point on the curve reflects the changing speed of the variable of the curve at that point.

The trend of the curve can still be described by the slope of the tangent of a point on the curve, which is the derivative. The geometric meaning of derivative is the tangent slope of function curve at this point.

F'(x)>0, the function increases monotonically in this interval, and the curve shows an upward trend; f '(x)& lt； 0, the function monotonically decreases in this interval, and the curve shows a downward trend.

In (a, b) f'' (x)