SOLUTION: Please help. Use the intermediate value theorem to determine whether g(x)=4x^3-3x+3 has a zero between -2 and -1. Thanks

Question 166553: Please help.
Use the intermediate value theorem to determine whether g(x)=4x^3-3x+3 has a zero between -2 and -1.
Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's evaluate the left endpoint

Start with the given equation.

Plug in .

Cube to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

-------------------------------------

Let's evaluate the right endpoint

Start with the given equation.

Plug in .

Cube to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So as x changes from -2 to -1, f(x) (or y) changes from -23 to 2 which means that the graph MUST have crossed over the x-axis somewhere in between x=-2 and x=-1. So this shows that there is a zero between x=-2 and x=-1
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