The title of Rolle's mean value theorem If the function f (x) = x & # 179 is continuous and differentiable in the interval [0,1], it is better to have a process

First of all, the elementary function is continuous in its domain, and the domain of F (x) = x ^ 3 is r, [0,1] is certainly included in the domain, so it is continuous. According to the derivation formula, f '(x) = 3x ^ 2 also exists in [0,1], so it can be derived

What is Rolle's mean value theorem?

Rolle's mean value theorem if the function f (x) satisfies: ① continuous on [a, b], ② differentiable in (a, b), and ③ f (a) = f (b), then there is at least one ξ ∈ (a, b) such that f '(ξ) = 0

The book is a plane equation with volume 9 of tetrahedron which is parallel to the plane 2x + y + 2Z + 5 = 0 and surrounded by three coordinate plane

Since the plane is parallel, let the equation of the plane be 2x + y + 2Z + C = 0, and the coordinates of the intersection of the three axes be x = - C / 2, y = - C, z = - C / 2 | 1 / 3 * C / 2 * c * C / 2 | = 9, C = 3 * 4 ^ (1 / 3)

Let f (x + 1 / x) = the third power of X + one third of X. find f (x)

X3 + 1 / X3 is what you call the third power of X + one third of X
Let x + 1 / x = X
The third power of (x + 1 / x) = (X3 + 1 / x3) + 2 (x + 1 / x) + (x + 1 / x), i.e
The third power of F (x + 1 / x) = X3 + 1 / X3 = (x + 1 / x) - 3 (x + 1 / x)
Let f (x) = the third power of X - 3x

P: A can be divided by 6 Q: B can be divided by 3
Please explain why?
What is the condition for P to be q

Sufficient and unnecessary conditions
For example, 18 can be divided by 6 and 3
Let's say 15, which is divisible by 3, but not by 6

Given that the distance from a point m on the ellipse x ^ 2 / 25 + y ^ / 9 = 1 to the right focus f is 8, n is the midpoint of MF, and O is the origin of the coordinate, then on is equal to?

Drawing shows that on is the median line of △ f1f2m, and MF2 = 2a-mf1 = 10-8 = 2, so on = 0.5mf2 = 1

The sum of the reciprocal of the three prime numbers is 19 / 165. What are the three prime numbers?
Come on, I need it badly

This is impossible. Let's take a look at their reciprocal sum. First of all, let's look at its denominator. The single digit is 5. Because in general division, only when one of the numbers is 5 as a single digit can we multiply 5. And the ones with 5 as a single digit are not prime numbers except 5. Because all of them can divide 5. So one of the prime numbers must be 5, In this way, we will find that 1 / 5 is larger than this number. And there is a way to know the reciprocal sum of prime numbers. Because the prime number has only its own factor and 1, then the denominator must be their product. Then the numerator is equal to a * B + b * C + A * C. here the denominator is 3 * 5 * 11, and the numerator is 3 + 5 + 11

A function has the following three properties: ① the function image passes through points (2, 3); ② the image is axisymmetric; ③ when the independent variable x > 1, the function value y decreases with the increase of X______ ．

When the independent variable x ＞ 1, the function value y decreases with the increase of X, then the opening of the image is downward, and the axis of symmetry can be a straight line x = 1. Then using the function image to pass through points (2, 3), the analytic formula of the function can be y = - x2 + 2x + 3. So the answer is y = - x2 + 2x + 3

As shown in the figure, the image of the inverse scale function y = KX (x > 0) passes through the intersection m of the diagonal of the rectangular oabc and intersects with AB and BC at points D and e respectively. If the area of the quadrilateral odbe is 6, then the value of K is______ ．

Let the coordinates of point m be (a, b), then k = AB, that is, y = ABX, ∵ point m is the intersection of diagonal lines of rectangular oabc, ∵ point a (2a, 0), C (0, 2b), B (2a, 2b), ∵ point d's abscissa is 2a, point e's ordinate is 2B, and ∵ point D and point e's ordinate is 12b on the image of inverse scale function y = ABX

If the sum of the digits in the Quaternary representation of a natural number is 5, and the sum of the digits in the pentanary representation is 4, then the remainder of the natural number divided by 3 is 4 The minimum natural number that meets the requirement is (decimal representation) ．

The sum of all digits is a pental number of 4, and the conversion between pental number, decimal number, quaternary number, quaternary number and 4 410 1 138 20 22 12 30 3 31 16 100 1 40 20 110 2 103

The title of Rolle's mean value theorem If the function f (x) = x & # 179 is continuous and differentiable in the interval [0,1], it is better to have a process