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December 18, 2014

December 18, 2014

Posted by **Anonymous** on Thursday, October 18, 2012 at 11:34am.

I.V.T.

*f(x) is continuous

*Lim x-> inf x^5+x+1 = inf >0

*Lim x-> -inf x^5+x+1 = -inf <0

Rolles

*f(c)=f(d)=0

*f(x) is coninuous

*f(x) is differentiable

f'(x) = 5x^4+1=0

As f'(x) does not equal zero, because of rolles theorem, the assumptioin f(x) has two roots is false.

Used Intermediate Value theorem and Rolles Theorm.

- Calculus (Please Check) -
**Damon**, Thursday, October 18, 2012 at 12:10pmyou mean f'(x) has no real roots I think.

It does cross the x axis at least once as you showed with intermediate value

however the slope is never zero so it never can cross the axis again. The other four roots are therefore complex numbers.

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