Does anyone know how to solve this with Intermediate Value Theorum? f(x)=3x^3-x-1; (0,1)

Question

Does anyone know how to solve this with Intermediate Value Theorum? f(x)=3x^3-x-1; (0,1)

Answer 1

f(x)=3x^3-x-1 ... Start with the given function.

f(0)=3(0)^3-0-1 ... Plug in the lower endpoint x=0

f(0)=-1 ... Evaluate and simplify

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f(x)=3x^3-x-1 ... Start with the given function.

f(1)=3(1)^3-1-1 ... Plug in the upper endpoint x=1

f(1)=1 ... Evaluate and simplify

Since the y-coordinate transitions from -1 to 1 on the interval (0,1), this means that there is a zero in the interval (0,1)