Values of the function y = 3^x − x^3 in the range [0,4] in steps of 0.25

Here are the values of the function \( y = 3^x - x^3 \) in the range \([0, 4]\) with steps of 0.25:

\[
\begin{array}{|c|c|}
\hline
x & y = 3^x - x^3 \\
\hline
0.00 & 1.000 \\
0.25 & 1.300 \\
0.50 & 1.607 \\
0.75 & 1.858 \\
1.00 & 2.000 \\
1.25 & 1.995 \\
1.50 & 1.821 \\
1.75 & 1.479 \\
2.00 & 1.000 \\
2.25 & 0.454 \\
2.50 & -0.037 \\
2.75 & -0.281 \\
3.00 & 0.000 \\
3.25 & 1.206 \\
3.50 & 3.890 \\
3.75 & 8.812 \\
4.00 & 17.000 \\
\hline
\end{array}
\]

Would you like more details on any specific part of this? 

Here are some related questions:

1. How does the function behave for values of \(x\) greater than 4?
2. What are the local minima and maxima in the interval \([0, 4]\)?
3. How does the derivative of the function change within the given range?
4. Can you identify points of inflection within this interval?
5. How would the function change if the power of 3 in \(3^x\) were altered?

**Tip:** Visualizing the function using a graph can provide a clearer understanding of its behavior.

Explore the values of the function y = 3^x − x^3 in the range from 0 to 4 with steps of 0.25. This problem covers exponential and polynomial functions, demonstrating their behavior within a specific interval. Suitable for students in Grades 10-12 studying advanced functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation