Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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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: 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(9869) About Me  (Show Source):
You can put this solution on YOUR website!
Let's evaluate the left endpoint x=-2


f(x)=4x^3-3x+3 Start with the given equation.


f(-2)=4(-2)^3-3(-2)+3 Plug in x=-2.


f(-2)=4(-8)-3(-2)+3 Cube -2 to get -8.


f(-2)=-32-3(-2)+3 Multiply 4 and -8 to get -32.


f(-2)=-32+6+3 Multiply -3 and -2 to get 6.


f(-2)=-23 Combine like terms.


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Let's evaluate the right endpoint x=-1


f(x)=4x^3-3x+3 Start with the given equation.


f(-1)=4(-1)^3-3(-1)+3 Plug in x=-1.


f(-1)=4(-1)-3(-1)+3 Cube -1 to get -1.


f(-1)=-4-3(-1)+3 Multiply 4 and -1 to get -4.


f(-1)=-4+3+3 Multiply -3 and -1 to get 3.


f(-1)=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