he graph of y​ = 5 x Superscript 6 Baseline minus 3 x Superscript 4 Baseline plus 2 x minus 9 has at most how many turning​ points?
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Part 1
Choose the correct answer below.
14
6
minus9
5

To determine the maximum number of turning points of a polynomial, we can use the following rule:

**A polynomial function of degree \(n\) can have at most \(n - 1\) turning points**.

The given function is:
\[
y = 5x^6 - 3x^4 + 2x - 9
\]
This is a 6th-degree polynomial (the highest exponent of \(x\) is 6).

Using the rule, the maximum number of turning points is:
\[
6 - 1 = 5
\]

Thus, the correct answer is:

**5**.

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Would you like further explanation or details on turning points? Here are some related questions for practice:

1. How do you find the actual turning points of a polynomial?
2. What is the difference between a turning point and an inflection point?
3. How does the derivative of a function help in finding turning points?
4. Can a 6th-degree polynomial have fewer than 5 turning points?
5. How can you use the second derivative to classify turning points?

**Tip:** The turning points occur where the derivative of the function equals zero.

The graph of y = 5x^6 - 3x^4 + 2x - 9 has at most how many turning points?

Discover how to calculate the maximum number of turning points for the 6th-degree polynomial y = 5x^6 - 3x^4 + 2x - 9. Learn about polynomial degrees and how to apply the rule for finding turning points. Suitable for students in Grades 10-12.

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