Use the intermediate value
posted by Ashley .
Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=4x^3+6x^27x+1; [4,2]
f(4)=

f(4) = 131
f(2) = 7
IVT says that f(x) assumes every value between 131 and 7 on [4,2]. In particular, there is some c in [4,2] where f(x) = 0.
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