Math Problem Statement

Consider the function  What are the coordinates of the maximum or minimum point of this function?

Question 14Answer

a.

(-4, -28)

b.

(4, 28)

c.

(4, -28)

d.

(-4, 28)

Solution

To determine the coordinates of the maximum or minimum point of a function, we generally examine its critical points or the vertex if it’s a quadratic function.

Without the explicit function, let's assume it's a standard quadratic form f(x)=ax2+bx+cf(x) = ax^2 + bx + c, where the maximum or minimum is located at the vertex of the parabola. The x-coordinate of the vertex can be found using:

x=b2ax = -\frac{b}{2a}

After substituting xx into the function, we find the y-coordinate.

If you provide the specific function, I can work through the exact calculations.

Let me know if you need further details, or if you’d like to review any of the following questions related to maximum and minimum points in functions:

  1. How to identify whether a point is a maximum or minimum.
  2. How to apply the derivative to find critical points in any function.
  3. How to verify concavity to confirm maximum or minimum points.
  4. How to apply the vertex formula for a general quadratic function.
  5. When to use first and second derivative tests for identifying extrema.

Tip: For quadratic functions, the vertex formula is a quick way to identify maximum or minimum points without needing derivatives.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Vertices of Parabolas

Formulas

Vertex formula x = -b / (2a) for quadratic functions

Theorems

Vertex of a Parabola Theorem

Suitable Grade Level

Grades 9-10