Question Prove that the function $f(x)=x^{7}+8 x-2$ has at most one real root using Rolle's Theorem. Show it has exactly one using the Intermediate Value Theorem.

Studdy Solution
Combining the results from Rolle's Theorem and the Intermediate Value Theorem, we conclude that $f(x)$ has exactly one real root.
The function $f(x) = x^7 + 8x - 2$ has exactly one real root.