SOLUTION: use the inermediate value theorem to determine, if possible, whether g(x)=4x^3-3x+3 has a zero between -2 and -1.

Question 121647: use the inermediate value theorem to determine, if possible, whether g(x)=4x^3-3x+3 has a zero between -2 and -1.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Let's evaluate

Start with the given function.

Plug in . In other words, replace each x with -2.

Evaluate to get -8.

Multiply 4 and -8 to get -32

Multiply -3 and -2 to get 6

Now combine like terms

-----------Now let's evaluate another value---------

Let's evaluate

Start with the given function.

Plug in . In other words, replace each x with -1.

Evaluate to get -1.

Multiply 4 and -1 to get -4

Multiply -3 and -1 to get 3

Now combine like terms

Since the y values transition from negative to positive as x goes from -2 to -1, this means there's a zero between -2 and -1
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