SOLUTION: Please assist me with the following problem:
Using the intermediate value theorem, determine, if possible, whether the function f has a real zero between a and b
f(x)=3x^2-2x
Algebra.Com
Question 165212: Please assist me with the following problem:
Using the intermediate value theorem, determine, if possible, whether the function f has a real zero between a and b
f(x)=3x^2-2x-11; a=2, b=3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's evaluate the left endpoint a=2
Start with the given equation.
Plug in .
Square to get .
Multiply and to get .
Multiply and to get .
Combine like terms.
------------------------------------------------
Let's evaluate the right endpoint b=3
Start with the given equation.
Plug in .
Square to get .
Multiply and to get .
Multiply and to get .
Combine like terms.
So as x changes from 2 to 3, f(x) (ie y) changes from -3 to 10 which means that the graph MUST have crossed over the x-axis somewhere in between x=2 and x=3. So this shows that there is a zero between a and b
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