Answer to Question #156973 in Calculus for Dar towseef

Question #156973

apply intermedaite value theorem on x^5-x^3+3x-5


1
Expert's answer
2021-01-21T20:09:30-0500

We denote by f(x) the function x5-x3 +3x-5.

f(x) tends to "+\\infty" when x tends to "+\\infty" and tends to "-\\infty" when x tends to "-\\infty"

Applying the intermediate value theorem, we have that this function takes any real values.


f(0)=-5<0 and f(x) tends to "+\\infty" when x tends to "+\\infty".

Applying the intermediate value theorem, we have that there exists a positive root of f(x).


f(1) = -2 < 0 and f(2) = 25 > 0

Applying the intermediate value theorem one time more, we have that one of the roots of f(x) lies in the interval (1,2).


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