Question

Исследуйте функцию и постройте ее график у=-4x^3+3x^2

Answer 1

Решение - в приложении

Answer 2

Function Analysis and Graph

The given function is u = -4x^3 + 3x^2. Let's analyze this function and plot its graph.

To analyze the function, we can start by looking at its degree and leading coefficient. The degree of the function is the highest power of x in the function, which is 3 in this case. The leading coefficient is the coefficient of the term with the highest power of x, which is -4 in this case.

The degree of 3 indicates that the function is a cubic function, and the negative leading coefficient (-4) suggests that the graph of the function will be concave down.

To plot the graph, we can start by finding the x-intercepts and y-intercept of the function.

To find the x-intercepts, we set u = 0 and solve for x:

-4x^3 + 3x^2 = 0

Factoring out x^2, we get:

x^2(-4x + 3) = 0

This equation is satisfied when either x^2 = 0 or -4x + 3 = 0.

Solving x^2 = 0, we find that x = 0 is a double root.

Solving -4x + 3 = 0, we find that x = 3/4.

Therefore, the x-intercepts of the function are x = 0 (with multiplicity 2) and x = 3/4.

To find the y-intercept, we set x = 0 and evaluate the function:

u = -4(0)^3 + 3(0)^2 = 0

Therefore, the y-intercept of the function is y = 0.

Now, let's plot the graph of the function.


Please note that the graph is a visual representation and may not be to scale. The x-axis represents the values of x, and the y-axis represents the values of u.

Conclusion

In conclusion, the function u = -4x^3 + 3x^2 is a cubic function with a concave-down graph. It has x-intercepts at x = 0 (with multiplicity 2) and x = 3/4, and a y-intercept at y = 0. The graph of the function can be plotted as shown above.