Question

Помогите пожалуйста! Исследовать функцию и построить ее график: f(x)=2x^2-x^4

Answer 1

f(x)=2x^2-x^4   четная   при х=0   у=0
f'(x)=4x-4x³=4x(1-x)(1+x)


-----------  -1-------------0---------------1--------------
       +                   -                 +                   -
возр.              уб.            возр.                 уб.
х=-1  макс.
х=0   мин.
х=1   макс.

Answer 2

Function and Graph Exploration: f(x) = 2x^2 - x^4

The given function is f(x) = 2x^2 - x^4. Let's explore this function and plot its graph.

To begin, let's analyze the function. It is a polynomial function of degree 4, which means it is a fourth-degree polynomial. The function is defined for all real numbers.

Now, let's plot the graph of the function f(x) = 2x^2 - x^4. To do this, we can use a graphing tool or software. Here is the graph:


The graph of the function f(x) = 2x^2 - x^4 is a downward-opening parabola that intersects the x-axis at x = -1 and x = 0. It reaches its maximum value at x = 0, where the y-coordinate is 0. The graph then decreases as x moves away from 0 in both positive and negative directions.

Please note that the graph image is not provided here, but you can use any graphing tool or software to plot the function and visualize its shape.

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