Consider the function $\displaystyle f(x)=6x^4-7x+1$ on the interval $\displaystyle [1/2,2].$ $\displaystyle f$ has at least one zero in $\displaystyle [1/2,2]$ (actually f(1)=0) so show that $\displaystyle f$ has *exactly* on zero in the indicated interval. Hint:Use the Mean Value Theorem/Rolle's Theorem to prove the result.