SOLUTION: Use the intermediate value theorem to show that the polynomial functions has zero in the given interval {{{ f(x) = 4x^3+3x^2-7x+7 }}}; [-4,-2]

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the intermediate value theorem to show that the polynomial functions has zero in the given interval {{{ f(x) = 4x^3+3x^2-7x+7 }}}; [-4,-2]      Log On


   

Question 937062: Use the intermediate value theorem to show that the polynomial functions has zero in the given interval
+f%28x%29+=+4x%5E3%2B3x%5E2-7x%2B7+; [-4,-2]
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The bounds of the interval are included. Check the signs of f%28-4%29 and f%28-2%29. If opposite, then z zero occurs between them on the interval.

A report of not being satisfied, here I explain, hopefully better:
The goal is to learn if f crosses the x-axis on the given interval. The bounds of the interval ARE INCLUDED. Let x be the left shown bound and evaluate f. Let x be the right shown bound and evaluate f. Now LOOK AT THE SIGNS of these f values. Compare this to what the Intermediate Value Theorem says.