Saturday, March 22, 2014

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 20

Sketch the graph of polynomial function $\displaystyle P(x) = \frac{1}{5}x (x - 5)^2$ make sure the graph shows all intercepts and exhibits the proper end behaviour.
The function has an odd degree 3 and a positive leading coefficient. Thus, its end behaviour is $y \rightarrow -\infty \text{ as } x \rightarrow -\infty \text{ and } y \rightarrow \infty \text{ as } x \rightarrow \infty$.
To solve for the $x$-intercept, we set $y = 0$.


$
\begin{equation}
\begin{aligned}
0 &= \frac{1}{5}x (x - 5)^2\\
\\
0 &= x \quad \text{and} \quad (x - 5)^2 = 0
\end{aligned}
\end{equation}
$


We have,
$x = 0$ and $x = 5$

To solve for the $y$-intercept, we set $x = 0$
$\displaystyle y = \frac{1}{5} (0) (0 - 5)^2 = 0$

No comments:

Post a Comment

Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...