Find the concave convex interval and inflection point of curve y = Xe ^ X / 2

Find the first derivative of a function and make it 0. The obtained x is the inflection point. Then look at the positive and negative values of the second derivative of the function at the neighborhood of the inflection point. If it is greater than 0, it is concave; if it is less than 0, it is convex

Why is a graph whose second derivative is greater than 0 why is it convex Please explain briefly

Why are curves with second derivative greater than 0 convex?
A more strict formulation is that the curve with the second derivative greater than 0 is convex downward, or concave upward. The arc formed by the chord of the curve and the arc between the chord and the chord is convex
If the convexity of a curve is defined in such a way that any chord of the curve does not intersect with the curve at the third point, then the main formulation is correct in this sense
This fact can be said intuitively that the second derivative reflects the change rate of the first derivative, and its constant greater than 0 indicates that the first derivative is constant increasing, that is, the tangent slope of the curve is increasing, that is to say, when the tangent of the curve slides from left to right along the curve, it rotates unidirectionally (anticlockwise), and there is no swing phenomenon. Therefore, the bow shape of the curve is convex
Simple proof (proof to the contrary): if the chord ab of a curve intersects with the curve at C points different from chord ends a and B, then according to Rolle's theorem, there is a tangent parallel to the chord on arc AC and arc BC, which contradicts the monotonous increase of tangent slope

What is the second derivative, its graph draws to have a look I want to draw the first and second derivative images, and the fourth-order function, and the meaning of the first and second derivatives,

If the original function is the distance time function, then the first derivative is the velocity time function, and the second derivative is the acceleration time function
You can try.

y=x(x-1)(x-2)(x-3)…… The n-th derivative of (x-n)

Observation y = x (x-1) (X-2) (x-3) (x-n)
The highest degree term of is x ^ (n + 1), which becomes (n + 1)! X after n-order derivation
The second highest order term is - (1 + 2 + 3 +...) +n) X ^ n, the coefficient is - n (n + 1) / 2
So the n-th derivative of Y is (n + 1)! X-n (n + 1) / 2

What is the physical meaning of the second derivative of deflection?

It is estimated that the building owner is talking about the mechanical design, which mostly adopts the small displacement theory, such as in the calculation of the bending deformation of the beam
In most cases, the actual deformation is very small, and the second derivative of deflection can approximately represent the curvature of beam axis, because the first derivative of deflection in curvature formula can be ignored
The purpose of this is to linearize the differential equation,

What is the physical meaning of derivative? For example, what else? More about it

I'm sorry, you said the opposite. The velocity (the rate of change of distance with time) is obtained by the derivation of distance, and the acceleration (the rate of change of velocity with time) is obtained by velocity derivation;
Derivation is the rate of change
There are other things that are similar. Every time you take a derivative, you get the rate of change of the physical quantity to be derived
Mathematically, every time a function differentiates according to the independent variable, the result is the change rate of the function with the independent variable

What is the mathematical and physical meaning of derivative?

(1) The geometric meaning of the derivative of a function at a point: shows the slope of the tangent line of the curve at the point
The physical meaning of the derivative of a function at a point: refers to the change rate of the function to the independent variable x. the second derivative of the function refers to the change rate of the independent variable x. the most commonly used instantaneous acceleration in physical quantities

Application of derivative physical meaning One is placed horizontally in the flume with a length of 12 meters and an isosceles trapezoid cross section. The bottom width is 3 meters, the mouth width is 9 meters, and the depth is 4 meters. Now water is injected at the speed of 10 cubic meters per minute. Try to find the rising speed of the water surface when the water depth is 2 meters

Let the velocity u = u (x, y), then what is the physical meaning of u seeking the partial derivative of X and the physical meaning of u seeking the second-order partial derivative of X?

The physical meaning of the partial derivative of u to X is that it represents the acceleration in the X direction
The physical meaning of the second order partial derivative of u to X is: the change speed of acceleration in X direction

How to derive implicit function It is used to solve the tangent line of the circle. Baidu Encyclopedia wrote that Leng did not understand, so ask, know how to teach thank you PS: I'm a sophomore in senior high school. I see that all the students are good at math. I've been out to compete in Olympiad. I haven't participated in it once. Of course, I can't pass the preliminaries unless I belittle myself.

1. The tangent equation of a circle -- the application of implicit function derivation: Circular equation: (x - X.) 2 + (Y - Y.) 2 = R 2 [analysis] from this equation, y = f (x) can be solved. Due to the square root, there is a sign problem

Find the concave convex interval and inflection point of curve y = Xe ^ X / 2