Answer
See explanations.
Work Step by Step
Step 1. $f(1)=4(1)^3-2(1)^2-7=-5\lt0$
Step 2. $f(2)=4(2)^3-2(2)^2-7=17\gt0$
Step 3. Based on the Intermediate Value Theorem, the function has a real zero in the given interval.
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