Question

F(x) = x3-3xпомогите​

Answer 1

Ответ:

x1=-√3

x2=0

x3=√3

Пошаговое объяснение:

f(x)=x³-3x

0=x³-3x

x³-3x=0

x*(x²-3)=0

x=0

x²-3=0

x=-√3

x=√3

Answer 2

Sure, I'd be happy to help you with the function F(x) = x^3 - 3x.

This function is a polynomial function of degree 3, also known as a cubic function. To better understand the properties and behavior of this function, we can analyze its graph, critical points, and other important aspects.

1. Graph of F(x): The graph of F(x) is a cubic curve. Cubic curves generally have an S-like shape. Since the leading coefficient (coefficient of x^3) is positive (1 in this case), the curve will rise on both ends as x approaches negative and positive infinity.

2. Critical points and local extrema: To find critical points, we need to determine where the derivative of the function F(x) is equal to zero. Let's find the derivative of F(x):

F'(x) = d/dx (x^3 - 3x) F'(x) = 3x^2 - 3

Now, set the derivative equal to zero and solve for x to find critical points:

3x^2 - 3 = 0 3x^2 = 3 x^2 = 1 x = ±1

So, the critical points are x = -1 and x = 1.

3. Nature of critical points: To determine whether these critical points are local maxima, local minima, or saddle points, we can use the second derivative test. The second derivative of F(x) is:

F''(x) = d^2/dx^2 (x^3 - 3x) F''(x) = 6x

Now, evaluate the second derivative at the critical points:

At x = -1: F''(-1) = 6(-1) = -6 (negative, so it's a local maximum) At x = 1: F''(1) = 6(1) = 6 (positive, so it's a local minimum)

4. Y-intercept and X-intercepts: The y-intercept is the value of F(0) when x = 0:

F(0) = 0^3 - 3(0) = 0

The y-intercept is 0.

To find the x-intercepts, set F(x) equal to zero and solve for x:

x^3 - 3x = 0 x(x^2 - 3) = 0

The solutions for x are: x = 0 (this is a repeated root, so there is a single x-intercept at x = 0) x^2 - 3 = 0 x^2 = 3 x = ±√3

So, there are two more x-intercepts at x = √3 and x = -√3.

5. Symmetry: The function F(x) is an odd function since it satisfies F(-x) = -F