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

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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=(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}

Determine roots,3)Describe end BehaviorDraw Quich Sketch.of polymonialf(x)=-77&quot-example-1
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