How to find the tangent equation of the derivative through a pointHow to find the tangent equation o

For example, y=x 2, and the tangent equation for (2,3) points is found using the derivative.

Let the tangent point (m,n), where n=m2

by y'=2x, the tangent slope k=2m

Tangent equations: y-n=2m(x-m), y-m2=2mx-2m2, y=2mx-m2

Because the tangent crosses the point (2,3), 3=2m*2-m2,m2-m2,m2-4m+3=0

m = 1 or m = 3

There are two tangents: m=1, y=2x-1; m=3, y=6x-9

To find the tangent equation of a point outside the curve, it is usually to set the tangent point first, write the tangent equation according to the tangent parameters, and then substitute the coordinates of the tangent point to find the tangent parameters, and finally write the tangent equation.

When the slope does not exist, the tangent point is the intersection of the center of the circle of the straight line parallel to the x-axis.

Extended information: Tangent equation is the study of tangent lines and the slope equation of tangents, involving geometry, algebra, physical vectors, quantum mechanics, etc. is the study of the relationship between tangent coordinate vectors of geometric figures.

The derivative of a function consisting of the sum, difference, product, quotient, or composite of the fundamental function can be derived from the derivative of the function. The basic derivative is as follows:

1. Linearity of derivation: Derivation of linear combination of functions is equivalent to finding the derivative of each part of the function and then taking the linear combination (i.e., formula).

2. The derivative function of the product of two functions: one derivative multiplied by two + one by two derivative (i.e. formula).

3. The derivative function of the quotient of two functions is also a fraction: (sub-derivative mother-child multiplication mother) divided by the female square (i.e., formula).

4. If there is a composite function, the derivative is obtained by the chain rule.

The derivative of a function at a point describes the rate of change of the function around that point. If both the independent variables and the values of the function are real, the derivative of the function at a point is the tangent slope of the curve represented by the function at that point.

The essence of derivatives is to perform a local linear approximation of a function through the concept of limits. For example, in kinematics, the derivative of the displacement of an object with respect to time is the instantaneous velocity of the object.

The derivative is used to find the tangent equation of the curve, which is also to find the derivative first, and then calculate the y value of the derivative, which is the slope of the tangent, combine the tangent point and the slope together, and find the tangent equation according to the point slope.

Finding the tangent equation of the curve is one of the important applications of the derivative, and the key to finding the tangent equation with the derivative is to find the tangent point p(o) and the slope, and the method is: let p(o,o) be a point on the curve y=f(x), then the tangent equation of the tangent point of p is: y-%=f'（x）x-）.

If the curve y=f() is defined by the tangent of the point p(xf() when the tangent of the point p(xf() is parallel to the y-axis (i.e., the derivative does not exist), the tangent equation is x=x·

Finding tangent equations is relatively easy content, and it is best not to make mistakes in this type of problem, it is a pity to lose points. If you want to find the extreme value, the most value, and need to be classified and discussed, you can find the derivative, and then find the zero point of the derivative, and then answer the question according to the actual situation.

The steps to find the tangent equation for a function image over a fixed point are as follows:

1) Set the tangent point to (x0,y0);

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

3) Write the tangent equation from the slope k and the tangent point (x0, y0) with the point oblique equation of the straight line;

4) Substituting the fixed-point coordinates into the tangent equation to obtain equation 1, substituting the tangent point (x0, y0) into the original function to obtain equation 2, solving the system of equations x0 and y0 by simultaneous equations 1 and equation 2, substituting the x0 and y0 coordinates into step 3) and simplifying the tangent equation obtained.

The point p(2,4) is on the curve, so it's a tangent point!

Derivative: y = x 2, x = 2, y = 4, this is the slope of the tangent, write the tangent equation with the point oblique formula.

Finding tangent equations for points that are not on a curve is more cumbersome and can sometimes be unsolvable.

Example: Change the midpoint of the above question to p(0,0)

a(a,a 3 3+4 3) is a point on the curve, use the above method to find the tangent equation of a is y-(a 3 3+4 3)=a 2(x-a), so that p(0,0) is on the tangent, get -(a 3 3 + 4 3)=-a 3, find a, and substitute the tangent equation.

1.It is known that the bai goes through the tangent equation and is outside the curve.

The coordinates of the du point zhi are (3,4) [the title will give]2Set the tangent coordinates to DAO(x0,y0).

3.Then the tangent is specialized.

The slope is y0-4 x0-3

4.The derivative of the original function y=f(x) is obtained.

5.Substitute x0 into the derivative.

6。Let the derivative function with x0 =y0-4 x0-3 be replaced by f(x0), and then solve the equation to calculate x0 8Knowing the slope of the tangent, knowing an abscissa (x0), can you calculate the tangent equation? Pure hand hope to adopt.

The expression of the curve function is known to be y=f(

x), the outer point of the curve is a(a,b).

Let the tangent point of the tangent be b(x0,y0).

So the tangent equation is: y-y0=f'(x0)(x-x0) and bring a(a,b) in:

Philately: b-y0=f'（x0）（a-x0）

L1 tangent the curve at point p, so L1 is the tangent of the curve at point p, and L2 is the tangent of the curve past point p.