\( [f(b)-g(b)]-[f(x)-g(x)]=\left[f^{\prime}(\xi)-g^{\prime}(\xi)\right](b-x) \geq 0 \) Al limite, per \( b \rightarrow+\infty \), otteniamo la tesi] l. 6 . Consideriamo per \( x>0 \) la funzione \( f(x)=\left(1+\frac{1}{x}\right)^{x} \). Utilizzando le, lisuguaglianze dell'esercizio 1.58 verificare che: (a) la funzione \( f(x) \) è strettamente crescente per \( x>0 \);

(2) \( f(x)=x^{3}-10 x^{2}-5 x+20 \) a) \( \int_{4}^{7} f(b)-f(a) \) b) \( 1^{\text {ra }} \) derivada c) Velocidad \( [5,8] \quad V_{m}=\frac{f\left(x_{f}\right)-f\left(x_{i}\right)}{V_{f}-x_{i}} \)

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) A. \( x=\square \) (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around. c) Find the \( y \)-intercept by computing \( f(0) \). (0) \( =\square \) d) Determine the symmetry of the graph. Odd; origin symmetry

Find the average rate of change of the function \( f(x)=x^{2}+9 x \) from \( x_{1}=1 \) to \( x_{2}=2 \). The average rate of change is \( \square \). (Simplify your answer.)

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) At which zeros does the graph of the function touch the \( x \)-axis and turn around? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x=\square \) (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around.

\begin{tabular}{l} (1) \( f(x)=3 x^{3}+2 x^{2}-5 x-10 \) \\ a) \( \int_{3}^{8} f(b)-f(a)= \) \\ b) Derivada \\ c) Velocidad \( \quad{ }_{m}=\frac{f\left(x_{i}\right)-f(x i)}{x_{f}-x_{i}} \quad[3,5] \) \\ \hline\end{tabular}