Mathematics: True or false. for a continuous function, of f(2) is negative and f(3) is positive, then there must be a zero between x=2 and x=3

True or false. for a continuous function, of f(2)

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erykp17

08.01.2022

Mathematics

It's true. In general, if a function is continuous, and you have

$f(x_1)=y_1,\quad f(x_2)=y_2$

then f(x) spans all the possible values between y_1 and y_2 in the interval [x_1,x_2]

So, in particular, if you have

$f(2) = y_2 < 0,\quad f(3) = y_3 0$

you can conclude that in the interval [2,3] , f(x) span all the values between y_2 and y_3 , which include 0 because y_2 is negative and y_3 is negative.

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True or false. for a continuous function, of f(2) is negative and f(3) is positive, then there must be a zero between x=2 and x=3

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