Verificare che, per ogni \( x>0 \), valgono le disuguaglianze (d) \( \quad x \log x \geq x-1 \) (b) \( \quad x \log _{a} x \geq(x-1) \log _{a} e \quad(a>1) \)

Differentiate. \( F(x)=\frac{1}{9 x-7} \)

Derivative DF \( F(x)=\frac{x}{\sqrt[3]{x^{2}+4}} \)

Determine the implied domain of the following function. Express your answer in interval notation.

Given the following function, determine the difference quotient, \( \frac{f(x+h)-f(x)}{h} \) \[ f(x)=x^{2}-7 x+3 \] Answer

On considère la fonction numérique \( f \) définie par: \[ f(x)=x-\sqrt{3-x^{2}} \] 1. Determiner \( D f \). \( \forall x \in D_{f} \quad f(x) \geq-2 \sqrt{3} \). 2. Montrer que : \( -2 \sqrt{3} \) est - il la valeur minimale de \( f \) sur \( D_{f} \).