Question Based on the degree of the polynomial $$ f(x) $$ given below, what is the maximum number of turning points the graph of $$ f(x) $$ can have? $$ f(x)=\left(x^{2}-7\right)\left(x^{2}-6\right)\left(x^{2}+4\right) $$ Provide your answer below:

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To determine the maximum number of turning points for the polynomial $$ f(x) = (x^{2} - 7)(x^{2} - 6)(x^{2} + 4) $$, follow these steps:

1. **Determine the Degree of the Polynomial:**
   - Each factor $$ (x^2 - a) $$ is a quadratic term with degree 2.
   - There are three such factors: $$ (x^{2} - 7) $$, $$ (x^{2} - 6) $$, and $$ (x^{2} + 4) $$.
   - Multiply the degrees: $$ 2 + 2 + 2 = 6 $$. 
   - Thus, $$ f(x) $$ is a 6th-degree polynomial.

2. **Maximum Number of Turning Points:**
   - A polynomial of degree $$ n $$ can have at most $$ n - 1 $$ turning points.
   - For $$ n = 6 $$: $$ 6 - 1 = 5 $$.

Therefore, the graph of $$ f(x) $$ can have a maximum of **5 turning points**.

**Answer:**  
5
The graph of $$ f(x) $$ can have a maximum of 5 turning points.

Question Based on the degree of the polynomial \( f(x) \) given below, what is the maximum number of turning points the graph of \( f(x) \) can have? \[ f(x)=\left(x^{2}-7\right)\left(x^{2}-6\right)\left(x^{2}+4\right) \] Provide your answer below:

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