Question
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Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=x^5-x^4+4x^3-4x^2-20x+18
[1.5,1.8]
Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=x^5-x^4+4x^3-4x^2-20x+18
[1.5,1.8]
Answers
Steve
f(1.5) = -4.96
f(1.8) = +0.77
Since f is continuous on the interval, and 0 is between -4.96 and +0.77, f must be zero somewhere in that interval. It cannot change from negative to positive without going through zero.
f(1.8) = +0.77
Since f is continuous on the interval, and 0 is between -4.96 and +0.77, f must be zero somewhere in that interval. It cannot change from negative to positive without going through zero.