College Algebra, Chapter 4, Chapter Review, Section Review, Problem 20

Graph the polynomial $P(x) = x^5 + x^4 - 7x^3 - x^2 + 6x + 3$ by using a graphing device. Find the $x$ and $y$ intercepts and the coordinates of all local extrema. Describe the end behavior of the polynomial.







Based from the graph, the $x$ intercepts can be approximated as $-3.05, 1.35$ and $1.80$. On the other hand, the value of the $y$ intercept is $3$. Also, the coordinates of the local maxima are $(-2.45, 33)$ and $(0.5, 5)$. While the coordinates of the local minima are $(-0.60, 0.80)$ and $(1.60, -1.75)$. More over, the function has an end behavior of $y \to \infty$ as $x \to \infty$ and $y \to - \infty$ as $x \to - \infty$.