Math Problem Statement

y=5x^(3)-9x^(2)+28x+6

Solution

You have the equation y=5x39x2+28x+6y = 5x^3 - 9x^2 + 28x + 6, which is a cubic function. Would you like to solve for xx, find its critical points, graph it, or do something else with it?

Here are some common operations you might want to explore with this function:

  1. Solve for xx when y=0y = 0 (finding the roots).
  2. Find the critical points (where the derivative is zero).
  3. Analyze the behavior of the function as xx \to \infty or xx \to -\infty (end behavior).
  4. Graph the function to visualize its shape.
  5. Find the inflection points to understand the concavity of the function.

Tip: A cubic function can have one or two turning points, depending on the nature of its critical points.

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Math Problem Analysis

Mathematical Concepts

Algebra
Cubic Functions
Derivatives
Critical Points
Inflection Points

Formulas

General form of a cubic equation: ax^3 + bx^2 + cx + d
First derivative: f'(x) = 15x^2 - 18x + 28
Second derivative: f''(x) = 30x - 18

Theorems

Fundamental Theorem of Algebra
Rolle's Theorem
First Derivative Test
Second Derivative Test

Suitable Grade Level

Grades 10-12