Math Solutions

[See Steps] Suppose that f: R \rightarrow R is C^1. Prove that f is concave if and only if f(x^*)+(x-x^*) f^prime(x^*) ≥q f(x), ∀ x and

Question: Suppose that \(f: R \rightarrow R\) is \(C^{1}\). Prove that \(f\) is concave if and only if \(f\left(x^{*}\right)+\left(x-x^{*}\right) f^{\prime}\left(x^{*}\right) \geq f(x), \forall x\) and \(x^{*}\)

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