Math Problem Statement

graph f(x)=x^4 - 4x^2 - x

Solution

Here is the graph of the function f(x)=x44x2xf(x) = x^4 - 4x^2 - x. You can observe the behavior discussed earlier, including the intercept at the origin and how the function grows rapidly as x|x| increases due to the x4x^4 term.

Would you like more details on how I derived certain points, or do you have any specific questions?

Here are five related questions:

  1. How do you find critical points and classify them as maxima, minima

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Math Problem Analysis

Mathematical Concepts

Polynomials
Graphing Functions
Critical Points

Formulas

f(x) = x^4 - 4x^2 - x
Derivative of f(x) for critical points: f'(x) = 4x^3 - 8x - 1

Theorems

First Derivative Test
Second Derivative Test

Suitable Grade Level

Grades 10-12