|What is the geometric meaning of X | and | x-a | ± | X-B |? As the title, as the title

|What is the geometric meaning of X | and | x-a | ± | X-B |? As the title, as the title

Combination of number and shape
|X | is the distance from the point x on the number axis to the origin
|X-a | + | X-B | is the sum of the distances from point x to point a and point B on the number axis
|X-a | - | X-B | denotes the distance difference from point x to point a and point B on the number axis

How to calculate left derivative and right derivative? What's the difference? What's the geometric meaning?

Let f (x) be defined in a field of points x0 and x0
If Lim [f (x0 + H) - f (x0)] / h exists, the limit is the right derivative of F (x) at x = x0. The left derivative is similar. The difference is that the direction of approximation is different

Is the third derivative geometric?

In general, only the first and second order derivatives have geometric meaning

Comprehensive application of geometric meaning of derivative
Given that the tangent line of the image with the function f (x) = (x ^ 2 / a) - 1 (a ≥ 0) at x = 1 is l, the minimum area of the triangle enclosed by L and two coordinate axes, the minimum area of the triangle, the minimum area of the triangle enclosed by L and two coordinate axes, and the minimum area of the triangle enclosed by L and two coordinate axes are obtained?
Explain the process in detail and use the derivative method
The detailed solution of straight line is OK

f'(x)=2x/a - 1
f'(1)=2/a - 1
f(1)=1/a - 1
Let the tangent equation l be y = KX + B, and substitute the tangent coordinates (1,1 / a - 1) and the slope f '(1)
1/a - 1 = (2/a - 1)x1+b
b=-1/a
The tangent equation l at x = 1 is y = (2 / a - 1) x - 1 / A
The intersection of tangent L and X axis is (1 / (2-A), 0)
The intersection of tangent L and Y axis is (0, - 1 / a)
The triangle area enclosed by tangent L and two coordinate axes s = 1 / (2-A) * (1 / a) / 2 = 1 / {2 [1 - (A-1) & # 178;]}
When a = 1, s min = (?) 189;

A derivative problem, investigate the geometric meaning of derivative and derivative
Given that the tangent L1 of curve y = alnx-1 (a ≠ 0) at point P (x0, Y0) passes through point (0, - 1)
For any nonzero real number a, it is proved that point P is on a definite line

Certification:
y'=a/x
The tangent equation through P is y-yo = A / XO × (x-xo)
Substituting (0, - 1), we get - 1-yo = A / XO × (- XO) = - A
That is, a = 1 + yo = 1 + (alnxo-1) = alnxo
And ∵ a ≠ 0, ∵ LNXO = 1, that is, XO = E
∴Yo=alnXo-1=a-1
That is, point P is always on the line x = E. for any a, the position of point P is (E, A-1)

Geometric problems of derivative
We know the curve C: y = 3x ^ 4-2x ^ 3-9x ^ 2 + 4. (1) find the tangent equation with the abscissa l of the tangent point on the curve C; (2) whether there are other common points between the tangent and the curve C in question (1)

From y = 3x ^ 4-2x ^ 3-9x ^ 2 + 4 to y '= 12x ^ 3-6x ^ 2-18x. X = 1, then y = 3-2-9 + 4 = - 4, y' = 12-6-18 = - 12
So the tangent equation of the abscissa 1 of the tangent point on the curve C is Y - (- 4) = - 12 * (x-1), that is 12x + Y-8 = 0
Consider the equation 12x + 3x ^ 4-2x ^ 3-9x ^ 2 + 4-8 = 0, that is, 3x ^ 4-2x ^ 3-9x ^ 2 + 12x-4 = 0
(x-1)^2*(x+2)(3x-2)=0
Obviously, there is a root X1 = 1, corresponding to the tangent point. The other two roots are x2 = - 1, X3 = 2 / 3
So the common points are (1, - 4) (tangent), (- 2,32), (2 / 3,0)
Besides the tangent point, there are two intersections (- 2,32) and (2 / 3,0)

The geometric meaning of the second derivative equal to 0? Such as the first-order function

Second derivative

What does this second derivative problem mean?
The title is as follows: F (X-Y, Y / x) = x ^ 2-y ^ 2, F "subscript is XX, how to solve this problem? What? Can you tell me in detail?
I just don't understand what "F" means when there are two X's
If we want to find the second derivative of X, shouldn't we use F "(x)?

The "F" subscript is XX, which means that the partial derivative of the given binary composite function is obtained for X first, and then the partial derivative of the obtained result is obtained for X, that is, the second-order partial derivative of the given binary function for the independent variable x is obtained

Given the square of function y = ax + C, when x = 3, the maximum value of function is 4, when x = 0, y = - 14, then its function expression is?

Simple

Enter a number from the keyboard and find the value of the piecewise function y = f (x). The expression of F (x) is as follows:
x+3 ,x>5
y = 0 ,0

int fnX(int x)
{
if(x>5)
return x+3;
else if(x>=0)
return 0;
else
return 2*x+30
}
main()
{
int data;
scanf("%d",&data);
printf("Result is %d\n",fnX(data));
}