Question

Chow do you use the intermediate value thm in Calculus AB

Answer 1

for what? you can use it for many things.

Answer 2

the problem just asks "use the intermediate value thm to show there is a root of the equation x3-3x+1=0 on the interval [0,1]

Answer 3

Since \(\large y=x^3-3x+1 \) is a polynomial (and therefore continuous for all x), evaluating the polynomial at x=0 and x=1 shows they have opposite signs. Therefore, they polynomial must have at least one zero in that interval.

Answer 4

Just to add to that:

The intermediate value theorem says if f(x) is continuous on [a,b] then there must me a number n where f(c)=n on (a,b) .

At 0 its 1 and at 1 its -1 so this must cross the x axis at least once. By the theorem there will exist at least some number where the y value is 0. (In other words, there is a solution.)