Answer
a. See explanations.
b. $x\approx-1.76929$, see graph.
c. $x≈-1.769292354$
Work Step by Step
a. Evaluate the function at the two values: $f(−2)=(−2)^3−2(−2)+2=−2\lt0$ and $f(0)=(0)^3−2(0)+2=2\gt0$. Based on the Intermediate Value Theorem, there must be a value $c$ in $(−1,2)$ such that$ f(c)=0$.
b. We can find the real solution graphically and identify the zero at $x\approx-1.76929$; see graph.
c. Using a calculator with enough precision, we can evaluate the exact answer as $x≈-1.769292354$; thus the answer in part (b) is very close to the exact value.
