The problem of finding tangent by derivative If the function y = f (x) passes through the tangent line of point P (x, f (x)), there are two cases, one is that the point is tangent point, the other is that the point is not tangent point, so there may be two answers My question is, isn't the tangent line only one intersection point with the image of y = f (x)? Since the point P (x, f (x)) is on y = f (x), isn't p the tangent point? If not, isn't the tangent point more than one intersection point with the image of y = f (x)?

Find the tangent line of the function y = f (x) passing through the point P (x0, f (x0)),
If y = f (x) is differentiable at point P, then f '(x0) exists, the slope of tangent exists, and of course tangent exists. P is the tangent point
If y = f (x) at point P when Δ x → 0, then Δ Y / Δ x →∞, the slope of tangent does not exist, but tangent exists. P is the tangent point
In other cases, P is not the cut-off point
Isn't the tangent a point of intersection with the image of y = f (x)?
This sentence should now read:
Isn't the tangent line just a point of intersection with the image of y = f (x) near point P?
Otherwise, the tangent of y = x ^ 3-x at x = √ 3 / 3 has two intersections with y = x ^ 3-x
It is correct to say that the graph of function y = f (x) has only one intersection point near the tangent point, and the tangent line has at least one intersection point in the definition domain

Elective course 1-1 mathematical conic curve and equation As shown in the graph, the point m (x, y) in the process of motion, always satisfies the relation formula x? 2 + (y + 3) 2 + X? 2 + (Y-3) - 10 under the root sign What curve is the locus of point m? Why? Write its equation Sorry, yes = 10, not - 10

That is, the sum of distances (x, y) to (0, - 3) and (0,3) is 10
So it's an ellipse
The two fixed points are the focus, on the y-axis
And C = 3
2a=10
A=5
So B 2 = a 2 - C 2 = 16
So x? 2 / 16 + y? 2 / 25 = 1

Given that the coordinates of points a and B are (- 1,0), (1,0), the straight line am and BM intersect at point m, and the difference between the slopes of line am and line BM is 2, then the trajectory equation of point m is () A. x2=-（y-1） B. x2=-（y-1）（x≠±1） C. xy=x2-1 D. xy=x2-1（x≠±1）

Let m (x, y), then KBM = y
x−1 （x≠1），kAM=y
x+1（x≠-1），
The difference between the slopes of line am and line BM is 2,
So Kam KBM = 2,
Y
x+1−y
x−1=2，（x≠±1），
X 2 + Y-1 = 0 (x ≠ ± 1)
Therefore, B

Conic curve and equation 4X² + Y² = 16 In this paper, we discuss the range of sub ellipse Is its elliptic equation x 2 + y 2 / 4=

Hello,
The ellipse is transformed into a standard equation x ^ 2 / 4 + y ^ 2 / 16 = 1
So in - 2 ≤ x ≤ 2, - 4 ≤ y ≤ 4
It's not the one below
Hope to help you!
Do not understand, please ask!
Hope to adopt!

In the triangle ABC, ab = C, AC = B, BC = a, and a > b > C, a, B, C form an arithmetic sequence. If vertices a and C are fixed points and | AC | = 2, the trajectory equation of point B satisfying the above conditions is obtained

From the known should use the definition method
Because a, B and C form an arithmetic sequence, a + C = 2B
And AC = 2, that is, B = 2, 2b = 4 = a + C = AB + AC, that is, the coordinates of point B satisfy the first definition of ellipse
And a, C are two focal points ·····················································································
The equation is so difficult to input oh... I should be able to write it out by myself, so I don't count it_ ∩)o
The answer above is not suitable for high school students

Important knowledge points in high school mathematics derivative Let's summarize

I don't know which province or province you are taking part in
Take Beijing as an example, half of the derivative of the college entrance examination is placed in the position of the penultimate question, and the score is about 13 points
If you want to get into a better university, you have to get a full score on derivative
So the problem of derivative is not too difficult
Pay special attention to the derivation of LNX, a ^ X and loga X
First of all, in the derivative problem in the examination, the derivative is mostly in the form of fraction, the denominator is usually constant > 0, and the numerator is generally quadratic function
Normally, the quadratic function is a function of quadratic coefficients with parameters
After that, we can start the classification discussion
Discussion point 1: discuss whether the coefficient of quadratic term is equal to 0
Of course, if the author is very kind, maybe it just doesn't exist
Here also should refer to the answer of the first question appropriately, the person who formulates the question will guide your thinking
Discussion point 2: Discussion △
For example, if the opening is upward, △ 0, then factorization can be considered
Normally, no one will ask you to use the root formula. It's meaningless to test this
Pay attention to the comprehensive application of classification discussion points 2 and 3, and draw a picture, thread the needle (pay attention to the negative sign) or directly draw the original function image, so the probability of error will be lower
We should pay attention to the calculation of derivatives. For example, if the roots are 1 / (a + 1) and 1 / (A-1), many people will be wrong if we discuss the two size problems of a on (0,1) and a on (1, + infinity)

Given that the function f (x) = ax LNX, if f (x) > 1, holds in the interval (1, + 00), find the value range of A

∵ f (x) = ax LNX > 1 and x > 1
∴a>(1+lnx)/x
Let g (x) = (1 + LNX) / X
g'(x)=((1/x)*x-(1+lnx))/x^2=-lnx/x^2
∵x>1
∴lnx>0
∴g'(x)

High school mathematics derivative knowledge summary

1. Simple derivation formula
2. Find monotone interval
3. Find the function extremum
4. Maximum value

A knowledge point of high school mathematics derivative Explain that "derivative must be continuous, continuous is not necessarily differentiable". By the way, what kind of situation does continuity refer to, and whether segmentation is continuous? Suppose f (x) = x (0 ≤ x < 1), f (x) = x + 1 (1 ≤ x ≤ 2), is f (x) a continuous function?

The continuity only requires that the left limit, the right limit and the function value of the point are equal. If the piecewise derivative function of a function exists, it is OK to satisfy this point, The left value of the derivative function on the piecewise point should be consistent with the value of the right derivative function. Note: the function expression of the derivative function on both sides of the piecewise point is not necessarily the same. Take a look at the basic definitions of continuity and derivation. There is no formula editor, we can only talk about it briefly

Ask high school mathematics derivative problem Find the derivative of y = X4 (the meaning of the fourth power) - x2-x-3 to help write the detailed process

solution
y=x^4-x^2-x-3
y'=(x^4)'-(x^2)'-(x)'-(3)'
y‘=4x³-2x-1