Math Problem Statement

can you fix the latex code it uneven when pasted:\documentclass{article} \usepackage{pgfplots} % For plotting graphs \usepackage{amsmath} % For advanced math typesetting \usepackage{caption} % For adding captions to figures

\pgfplotsset{compat=1.18} % Adjust this to match your Overleaf version

\begin{document}

\begin{center} \LARGE{3D Plot of a Polynomial Function}$$1em] \normalsize{In this figure, we present a 3D plot of the polynomial function}

[ f(x, y) = x^3 + 2x^2 - 5x + 7 + y^3 + 2y^2 - 5y + 7

\normalsize{This function combines cubic and quadratic terms in both $$ x $$ and $$ y $$, resulting in a complex surface. The plot visualizes how the function behaves over the domain $$ x, y \in [-3, 3] $$. The color gradient on the surface represents different function values, helping to highlight the peaks and troughs of the surface.} \begin{figure}[h] \centering \begin{tikzpicture} \begin{axis}[ axis lines = middle, xlabel = {$x$}, ylabel = {$y$}, zlabel = {$f(x, y)$}, domain=-3:3, y domain=-3:3, samples=30, grid=major, width=10cm, height=10cm, zmin=-15, zmax=20, xlabel style={below right}, ylabel style={below left}, zlabel style={above}, colormap/cool, ] \addplot3[ surf, shader=interp, ] {(x^3 + 2*x^2 - 5*x + 7) + (y^3 + 2*y^2 - 5*y + 7)}; \addlegendentry{$f(x, y) = x^3 + 2x^2 - 5x + 7 + y^3 + 2y^2 - 5y + 7$} \end{axis} \end{tikzpicture} \caption{3D plot of the function $$ f(x, y) = x^3 + 2x^2 - 5x + 7 + y^3 + 2y^2 - 5y + 7 $$. The plot shows the surface over the domain $$ x, y \in [-3, 3] $$ with color indicating the value of the function.} \end{figure} \vspace{1em} \normalsize{This type of 3D plot is useful for visualizing functions of two variables, where the surface represents the value of the function for each pair of $$ x $$ and $$ y $$. The use of a color map helps in identifying regions of high and low values, providing more insight into the function's behavior.} \end{center} \end{document}

Solution

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Math Problem Analysis

Mathematical Concepts

Polynomial functions
3D plots
Surface visualization

Formulas

f(x, y) = x^3 + 2x^2 - 5x + 7 + y^3 + 2y^2 - 5y + 7

Theorems

-

Suitable Grade Level

Advanced