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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let's evaluate the left endpoint x=-2


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


f%28-2%29=4%28-2%29%5E3-3%28-2%29%2B3 Plug in x=-2.


f%28-2%29=4%28-8%29-3%28-2%29%2B3 Cube -2 to get -8.


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


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


f%28-2%29=-23 Combine like terms.


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Let's evaluate the right endpoint x=-1


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


f%28-1%29=4%28-1%29%5E3-3%28-1%29%2B3 Plug in x=-1.


f%28-1%29=4%28-1%29-3%28-1%29%2B3 Cube -1 to get -1.


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


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


f%28-1%29=2 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