Question

СРОЧНО, помогите! Исследовать функцию и построить ее график y=2x^3-6x+2

Answer 1

D(y)∈(-∞;∞)
y(-x)=-2(-x)²+6(-x)-3=-2x²-6x-3-ни четная ни нечетная
Точки пересечения с осями
x=0⇒y=-3
y=0⇒-2x²+6x-3=0
D=36-24=12
x1=(-6-2√3)/-4=(3+√3)/2 x2=(3-√3)/2
(0;-3),((3+√3)/2;0),((3-√3)/2;0)
y`=-4x+6=0
x=1,5
+ _
___________________________
возр 1,5 убыв
max
ymax=-2(1,5)²+6*1,5-3=-2*2,25+9-3=-4,5+6=1,5

Answer 2

Function Analysis and Graph Plotting for y=2x^3-6x+2

To analyze the function y=2x^3-6x+2 and plot its graph, we can follow these steps:

1. Function Analysis: - The function is in the form y=2x^3-6x+2. - The derivative of the function can be calculated to find critical points and inflection points.

2. Graph Plotting: - We can plot the graph of the function y=2x^3-6x+2 to visualize its behavior and characteristics.

Function Analysis:

The derivative of the function y=2x^3-6x+2 is: y' = 6x^2 - 6

Graph Plotting:

Let's plot the graph of the function y=2x^3-6x+2 to visualize its behavior and characteristics.

import numpy as np
import matplotlib.pyplot as plt

# Define the function
def f(x):
    return 2*x**3 - 6*x + 2

# Generate x values
x = np.linspace(-5, 5, 400)
# Generate y values
y = f(x)

# Plot the graph
plt.figure(figsize=(8, 6))
plt.plot(x, y, label='$y=2x^3-6x+2$', color='b')
plt.title('Graph of y=2x^3-6x+2')
plt.xlabel('x')
plt.ylabel('y')
plt.grid(True)
plt.axhline(0, color='black',linewidth=0.5)
plt.axvline(0, color='black',linewidth=0.5)
plt.legend()
plt.show()

The graph of the function y=2x^3-6x+2 will provide a visual representation of its behavior and characteristics.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.