Question

use rolle's theorem to show that the equation 7x^6-9x^2+2=0 has at least one solution in the interval (0,1)

Answer 1

let f(x) = 7x^6-9x^2+2
f(0) = 2
f(1) = 7-9+2 = 0 , well , isn't that special, we accidentally found a solution

So I guess there has to be at least one solution.