Question: Suppose that \(f(x)\) has a continuous first derivative for all \(x \in R\)

1. Prove that \(f(x)\) is concave if and only if \(f\left(x^{*}\right)+\left(x-x^{*}\right) f^{\prime}\left(x^{*}\right) \geq f(x)\) for all \(x\) and \(x^{*} \in R\).
2. Given that \(f(x)\) is concave, prove that \(x^{*}\) is a global maximum of \(f(x)\) if and only if \(f^{\prime}\left(x^{*}\right)=0\).
3. Given that \(f(x)\) is strictly concave, prove that it cannot possess more than one global maximum.

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document