Question

Determine roots,3)Describe end BehaviorDraw Quich Sketch.of polymonialf(x)=-77" + 2X

Answer 1

Given the function:

$f(x)=-7x^4+2x^3$

the sketch of the function will be as shown in the following picture

The roots of the function are the value of x which make f(x) = 0

As shown in the figure :

The roots are x = { 0 , 2/7 }

We can find the roots without graph by the factor the given function as follows:

$\begin{gathered} -7x^4+2x^3=0 \\ x^3\cdot(-7x+2)=0 \\ \\ x^3=0\rightarrow x=0 \\ or\text{ } \\ -7x+2=0\rightarrow x=\frac{2}{7} \end{gathered}$

The end behavior:

$\begin{gathered} x\rightarrow\infty,f(x)\rightarrow-\infty \\ x\rightarrow-\infty,f(x)\rightarrow-\infty \end{gathered}$