Question

Построить график в f(x)=3x^2-x^3

Answer 1

Просто придумай любые числа вместо х. Например:
х= -3, -2, 0, 2, 3
f(-3)= 3*(-3)*2-(-3)*3=-18-(-9)=-9 
9 это у
Потом решаешь всё также, подставляя х, рисуешь на координатной плоскости точки(х;у) и соединяешь.

Answer 2

Graph of f(x) = 3x^2 - x^3

To plot the graph of the function f(x) = 3x^2 - x^3, we can start by analyzing the equation and identifying key points.

The equation f(x) = 3x^2 - x^3 is a polynomial function of degree 3. This means that the graph will be a curve.

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

3x^2 - x^3 = 0

Factoring out an x, we get:

x(3x - x^2) = 0

Setting each factor equal to zero, we find two x-intercepts:

x = 0 and x = 3

To find the y-intercept, we set x equal to zero:

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

So the y-intercept is at the point (0, 0).

We can also find the critical points by taking the derivative of the function and setting it equal to zero:

f'(x) = 6x - 3x^2

Setting f'(x) equal to zero, we get:

6x - 3x^2 = 0

Factoring out an x, we have:

x(6 - 3x) = 0

Setting each factor equal to zero, we find two critical points:

x = 0 and x = 2

Now, let's plot the graph of f(x) = 3x^2 - x^3:


The graph of f(x) = 3x^2 - x^3 is a downward-facing curve that intersects the x-axis at x = 0 and x = 3. The y-intercept is at the point (0, 0). The critical points are at x = 0 and x = 2.

I hope this helps! Let me know if you have any further questions.