Patrick B. answered • 09/06/19
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Math and computer tutor/teacher
f(x) = x^3 - 2^x
a=1.25 b = 1.375
f(1.375) = 0.0059302657-
f(1.25) = -0.42528923+
The function is continuous on the interval
and has opposite signs, Therefore IVT guarantees
a solution where f(x)=0 on the interval
f(1.5) = -1.322712+
Once again the function has opposite signs on
the interval [1.375, 1.5) so another solution
f(x)=0 exists by IVT
John N.
^^ Correction: f(1.5)=0.54657, and thus there is only one solution in the interval [1.25, 1.375]. The second solution doesn't exist because 0 does not fall between f(1.375) and f(1.5).01/21/21