Find the average value of \( f(x)=x^{4} \) on the interval \( [5,7] \). Leave your answer as a fraction. The average value is:

Differentiate. (Hint: Use the Extended Power Rule.) \( g(x)=(\ln x)^{4} \)

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

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

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

Find the general form of \( f \) if \( f^{\prime}(x)=8 f(x) \).