Math Problem Statement

Find the properties of the function f(x) = x^3 - 6x^2 + 9x.

Solution

The function shown in the image is:

f(x)=x36x2+9xf(x) = x^3 - 6x^2 + 9x

Would you like to analyze it in any specific way, such as finding its derivative, critical points, or anything else?

Let me know how you'd like to proceed! Here are some related questions for further exploration:

  1. Would you like to find the derivative of this function?
  2. Are you interested in finding the critical points where the derivative is zero?
  3. Would you like to analyze the function’s concavity and inflection points?
  4. Do you want to determine the local maxima and minima of the function?
  5. Should we evaluate this function for specific values of xx?

Tip: Understanding the behavior of a function through its first and second derivatives can provide insights into its increasing/decreasing intervals and concavity patterns.

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Critical Points
Concavity

Formulas

First Derivative f'(x)
Second Derivative f''(x)

Theorems

First Derivative Test
Second Derivative Test

Suitable Grade Level

Grades 10-12