How to draw 4x square - 96x + 572 function image There are also lists

How to draw 4x square - 96x + 572 function image There are also lists

From the analytical formula, y = 4x ^ 2-96x + 572 = 4 (X-13) (X-11), we can see that the image and Y axis intersect at (0572) and X axis intersect at (11,0), (13,0) can be drawn from this
According to what you mean, it should be a list drawing
Then order in turn
X = 9,10,11,12,13 and so on, then get the corresponding y, trace the points on the coordinate axis in turn, and then connect them with smooth curves

It is proved that the function FX = x + 4 / X is a monotone increasing function in the interval (2, positive infinity)

Certification:
Order 2 "X1"

Let f (x) = (x + a) / (x + b) and (a > b > 0). Find the monotone interval of F (x) and prove it

Decreasing on R
Proof: the derivative function is less than 0

Monotonicity of functions with derivatives equal to 0

If the derivative is directly equal to zero, there is no monotonicity
In a function, if x makes the derivative equal to zero, then the point corresponding to X is the extremum of the function. If the extremum is preceded by an increasing function and followed by a decreasing function, it is the maximum; otherwise, it is a decreasing function. If both the increasing and decreasing functions are the extremum, it is not the extremum=

Is the monotonicity of derivative function consistent with that of original function?
That is to say, can we get the monotonicity of the function after integration directly from the monotonicity of the integrand?
For example, if the integrand is an increasing function, then its integral is also increasing?
E ^ u is an increasing function on (0,1), so ∫ e ^ x > ∫ e ^ x ^ 2?

No, there is no direct relationship. Many counter examples are y = x ^ 2, y '= 2x. On X ∈ R, the original function is not monotone, and the derivative function is monotone. Another example is y = x ^ 3, y' = 3x ^ 2. On X ∈ R, the original function is monotone, and the derivative function is not monotone. Therefore, there is no relationship

How to judge the monotonicity of function?

Compound function
Functions can be reduced to several single functions
For example, y = 4 / (x + 5)
We can see it as the combination of y = 5 / X and y = x + 5
Then determine the monotone interval of two functions respectively. Of course, the former one is just an example. In fact, it is generally more complex than that one
After the monotone interval of a single function is determined, the intersection is obtained
For example: the monotone interval of the first single function is
(3,6) increasing, [6,12) decreasing, (13,15) increasing (assuming this is the domain)
The monotone interval of the second function is (3,12) monotone decreasing, (13,15) increasing
So we're going to take their monotonic intersection
Because the decreasing interval of the second function is (3,12)
And the first one happens to be (3,6) and [6,12]
Then it can be directly divided into three sets (3,6), (6,12), (13,15)
The first set is increase or decrease (that is, the first function is increase and the second function is decrease)
And so on, the second set is subtraction, and the third set is increment
There is a theorem that the monotonicity of compound functions is
More is more
Decrease and increase
Increase or decrease
In fact, it is the multiplication of positive and negative signs. Positive results in positive and negative results in positive
The key is to find the intersection of a single function and a pair

The relationship between function monotonicity and function maximum

The monotonicity of function describes the value changing trend of function in the domain of definition
For a function whose domain is r, monotonicity determines whether the function has a maximum or a minimum. However, the maximum value of a function depends on monotonicity and domain. In a specific domain, it can be said that any function has a maximum

If the domain x belongs to R and the function f (x) satisfies f (x-1) = f (2-x), then the axis of symmetry is?

Let x = 3 / 2-y and substitute f (1 / 2-y) = f (1 / 2 + y), that is, its axis of symmetry is x = 1 / 2

The concept of parity of mathematical function in grade one of senior high school, judging parity, seeking process, seeking thinking
It is known that f (x) is a function defined in the range of real numbers. For any x, y belonging to R, f (x + y) + F (X-Y) = 2F (x) f (y), and f (0) ≠ 0
Verification: F (0) = 1
Judge the parity of function

It is proved that f (x + y) + F (X-Y) = 2F (x) f (y), f (0 + 0) + F (0-0) = 2F (0) f (0) 2F (0) = 2F (0) * f (0) f (0) [f (0) - 1] = 0 ∵ f (0) ≠ 0. It is proved that f (x + y) + F (X-Y) = 2F (x) f (y) let x = 0, then f (y) + F (- y) = 2F (0) * f (y) = 2F f (y), f (y)

How to judge whether the domain of F (x) is symmetric about the origin? For example?

If the domain is all real numbers, it must be symmetric about the origin
If the domain is not all real numbers, such as all positive real numbers, then the domain can't be valued on the negative half axis of X axis, let alone symmetric
For another example, if the domain is all negative real numbers, then the domain can't take value on the positive half axis of X axis, so the domain is not symmetric about the origin
For example: F (x) = 1 / (1-x) the definition field of this problem is that x is not equal to 1, then if the definition field is symmetric about the origin, X cannot be equal to - 1
Let's take another example: F (x) = even root of X. The definition field of this problem is x nonnegative, X nonnegative, and the symmetric interval about the origin is x nonpositive
So the domains in both cases are not symmetric about the origin
Generally, when we discuss the parity of a function, we will pay attention to the value of the domain. If the domain is symmetric about the origin, the function can be odd or even. If a function's domain is not symmetric about the origin, it is not qualified to be odd or even