hello i need help with this calculus 1 homework, its kinda difficult, thank you!

EXAMPLE 10 Show mat there is a solution of the equation 4x3 7 6x2 + 3x 7 2 = 0 between 1 and 2. SOLUTION Let x) 2 4x3 Eu:2 + 3x 2 = Cl. We are looking for a solution of the given equation, that is, a numberc between 1 and 2 such that (c) = |:| X . Therefore we take a = 1, b = |:| x , and N = |:| x in the Intermediate Value Theorem. We have r(1)=46+32=1u. Thus, f(1) o. Based on these inequalities, a solution lies in the open interval, in interval notation