Answer to Question #156973 in Calculus for Dar towseef

Question

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

Answer 1

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).