suppose the function f(x)=50-9x+x^4/30 describe a physical situation that makes sense only for whole numbers between 0 and 10. For what value of x does f each a minimum, and what beginning with a table starting at 0 with a table increment of  1 and then panning further down the table. give me a table

Here is the table showing the values of \( f(x) = 50 - 9x + \frac{x^4}{30} \) for \( x \) from 0 to 10, with an increment of 1:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 50.00 \\
1 & 41.03 \\
2 & 32.53 \\
3 & 25.70 \\
4 & 22.53 \\
5 & 25.83 \\
6 & 39.20 \\
7 & 67.03 \\
8 & 114.53 \\
9 & 187.70 \\
10 & 293.33 \\
\hline
\end{array}
\]

The function \( f(x) \) reaches a minimum at \( x = 4 \), where \( f(4) = 22.53 \).

Would you like further details or have any questions?

Here are 5 related questions to think about:
1. What is the physical interpretation of this minimum in a real-world scenario?
2. How would the behavior of the function change if the coefficients were slightly different?
3. What does the derivative of this function look like, and how can it confirm the minimum?
4. Can you estimate the concavity of the function around the minimum?
5. What would the behavior be if the range of \( x \) values extended beyond 10?

**Tip:** Always check the domain of the problem and if the function makes sense within that range.

suppose the function f(x)=50-9x+x^4/30 describe a physical situation that makes sense only for whole numbers between 0 and 10. For what value of x does f each a minimum, and what beginning with a table starting at 0 with a table increment of 1 and then panning further down the table. give me a table

Explore how to find the minimum value of the polynomial function f(x) = 50 - 9x + x^4/30 for integer values of x from 0 to 10. Includes a detailed table of values, analysis of the function's behavior, and the use of calculus to confirm the minimum at x = 4.

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