Answer
See below.
Work Step by Step
1. Given $f(x)=4(x)^3-2(x)^2-7$, we have $f(1)=4(1)^3-2(1)^2-7=-5\lt0$ and $f(2)=4(2)^3-2(2)^2-7=17\gt0$.
2. Based on the Intermediate Value Theorem, there should be at least one real zero in the interval $[1,2]$.
