SOLUTION: Calculus Question
Use the Intermediate Value Theorem and Rolle's Theorem to determine that {{{ f(x)=x^7+4x^5+3x+5 }}} has exactly one real root between -1 and 0.
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Question 1142316: Calculus Question
Use the Intermediate Value Theorem and Rolle's Theorem to determine that has exactly one real root between -1 and 0.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If a function 
is continuous on the closed interval 
and has values )
and )
at each end of the domain interval, then the function takes on any value in the interval ,f(b)\])
at some point in the domain interval.
All polynomial functions with real coefficients are everywhere continuous.
\ =\ x^7\ +\ 4x^5\ +\ 3x\ +\ 5)
is a polynomial function with real coefficients and is therefore everywhere continuous and is therefore continuous on the interval 
.
\ =\ -3)
\ =\ 5)
Therefore )
has any value in the interval 
for some 
therefore \ =\ 0)
John
My calculator said it, I believe it, that settles it
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