How to judge the continuity of function with derivative

If the function y = f (x) is differentiable at x0, then f (x) is continuous at x0
In other words, the continuity of function f (x) at point x0 is a necessary but not sufficient condition for f (x) to be differentiable at x0

Is there a necessary connection between the continuity of function and derivative?

For example, y = | x | is a continuous function, but it is not differentiable at y = 0
The derivation must be continuous
Let the function y = f (x) be differentiable at point x, that is, its derivative exists. From the relationship between the function with limit and infinitesimal, we know that △ Y / △ x = f '(x) + B, B is the infinitesimal when △ x tends to infinity, and the above formula is obtained by multiplying △ X
It can be seen that when △ x tends to 0, △ y tends to 0
Y = f (x) is continuous at point X. therefore, if the function y = f (x) is differentiable at point x, then the function must be continuous at that point

Given that angle ABC = angle ADC = 90 degrees and E is the midpoint of AC, is EBD equal to angle EDB
process

The topic is not complete. What is the relationship between angle ABC = angle ADC in position?

If a is not equal to 0, a and B are opposite numbers, then the inequality ax + B

b=-a
So B / a = - 1
-b/a=1
ax0,x

In the parallelogram ABCD, the module of AB is 4, the module of ad is 3dab is 60 degrees. Find the vector ad times the vector BC, the vector AB times the vector CD, the vector AB times the vector da
But I can't judge the angle

In the parallelogram ABCD, vector ad = vector BC, vector AB = vector DC,
Vector ad times vector BC = vector ad times vector ad = 3 * 3 = 9
Vector AB multiplied by vector CD = vector AB multiplied by vector Ba = vector AB multiplied by (- vector AB) = - 4 * 4 = - 16
Vector AB multiplied by vector Da = vector AB multiplied by (- vector AD) = - vector AB multiplied by modulus of vector ad = - AB multiplied by modulus of ad cosdab
=-4*3*（1/2）=-6

There are six numbers in a row, and their average number is 27. It is known that the average number of the first four numbers is 23, the average number of the last three numbers is 34, and the fourth number is 27______ ．

23 × 4 + 34 × 3-27 × 6, = 92 + 102-162, = 194-162, = 32

Experiment of parallelogram rule to verify force
Why should the F1F2 angle not be large or small,
In addition, some books say that two spring dynamometers must have the same reading (that is, F1F2 must be equal in size),

If the F1F2 angle is too large, the resultant force is too small, which will increase the experimental error;
If the F1F2 angle is too small (close to 0), it is not a parallelogram
The reading of two spring dynamometers need not be the same. The purpose of the experiment is to "verify the parallelogram rule of force". It is a special case to control two real numbers to be the same, which should not be controlled in this way

If a car travels less than 20 kilometers per hour from place a to place B, it will take 1 / 4 more time than the scheduled time; if the speed increases by 1 / 5, it will take 1 hour less than the scheduled time. How many kilometers are there between a and B? (hint: the first condition can get the time ratio, the speed ratio, and then the speed; the second condition can use the previous method, and then the time.)

The time is 1 / 4 more than the scheduled time, and the ratio with the scheduled time is (1 + 1 / 4): 1 = 5:4
The ratio of speed to original speed is 4:5
The original speed is 20 (5-4) × 5 = 100 km / h
The speed is increased by 1 / 5, and the ratio to the original speed is (1 + 1 / 5): 1 = 6:5
The ratio of required time to scheduled time is 5:6
The scheduled time is: 1 △ (6-5) × 6 = 6 hours
Distance between a and B: 100 × 6 = 600 km

If the quadratic function f [x] = x square - [a + 2] x + 5 is increasing in the interval [1 / 2,1]
1. Find the value range of A
2. Let G [a] = f [2A], find the range of G [a]

1. Function image opening up
First find the axis of symmetry x = (a + 2) / 2
In order to increase monotonically in the interval [1 / 2,1], the axis of symmetry must be on the left side of the interval [1 / 2,1]; that is, the axis of symmetry must be on the left side of the interval [1 / 2,1]
(a+2)/2

Given the function f (x) = e ^ x-ex. find the minimum value of F (x)

The derivative is e ^ x-e, and the zero point is x = 1. Then we can see that the second derivative e ^ x is greater than zero. Therefore, the minimum value of the function at x = 1 is 0

How to judge the continuity of function with derivative