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

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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(21667) About Me  (Show Source):
You can put this solution on YOUR website!

Let's evaluate g%28-2%29


g%28x%29=4x%5E3-3x%2B3 Start with the given function.


g%28-2%29=4%28-2%29%5E3-3%28-2%29%2B3 Plug in x=-2. In other words, replace each x with -2.


g%28-2%29=4%28-8%29-3%28-2%29%2B3 Evaluate %28-2%29%5E3 to get -8.


g%28-2%29=-32-3%28-2%29%2B3 Multiply 4 and -8 to get -32


g%28-2%29=-32%2B6%2B3 Multiply -3 and -2 to get 6


g%28-2%29=-23 Now combine like terms




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


Let's evaluate g%28-1%29


g%28x%29=4x%5E3-3x%2B3 Start with the given function.


g%28-1%29=4%28-1%29%5E3-3%28-1%29%2B3 Plug in x=-1. In other words, replace each x with -1.


g%28-1%29=4%28-1%29-3%28-1%29%2B3 Evaluate %28-1%29%5E3 to get -1.


g%28-1%29=-4-3%28-1%29%2B3 Multiply 4 and -1 to get -4


g%28-1%29=-4%2B3%2B3 Multiply -3 and -1 to get 3


g%28-1%29=2 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