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Given an interval $[a,b]$ that satisfies hypothesis of Rolle's theorem for function $f(x) = x^4 + x^3 - x^2 + x -2$

If $a = -2$, how do I find $b$ ?

This is what Ive done so far, Not sure if it is right...

Rolles theorem says if $f(a)=f(b)$ at some point in the interval $[a,b]$ the derivative of the function is zero.

so,$f(a)=32-8-8-4=12$

Lets find a $b$ where $f(b)=12$

so, $f(b)=b^4+b^3-b^2+b-2=12$

This is hard to do, but wolfram alpha says $b=1.77$

So somewhere between $-2$ and $1.77$ the derivative is zero.

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    Once you have the correct $f(a)$, you might want to check $b=1$.2012-04-02

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Since $f$ can be rewritten as $f(x) = (x-1)(x+2)(x^2+1)$, you can see that $f(-2) = f(1)$. There is a local extremum somewhere in $(-2,1)$.