The total cost function for a product is \[ C(x)=750 \ln (x+10)+1700 \] where \( x \) is the number of units produced. (a) Find the total cost of producing 300 units. (Round your answer to the nearest cent.) \( \$ \) (b) Producing how many units will give total costs of \( \$ 7500 \) ? (Round your answer to the nearest whole number.) units

\( \int \frac { 1 + \sin x } { 1 + \cos x } e ^ { x } d x \)

Whsider the function \( f \) defined by \( f(x)=x^{4}-4 x^{3} \). What is the domain of \( f \). Determine the \( x \)-intercept(s) and \( y \)-intercept? Find \( f^{\prime}(x) \). Determine the interval(s) where \( f \) increasing? decreasing? Identify the points of local maxima or/and minima and determine their values if exist? Find \( f^{\prime \prime}(x) \). Identify the interval(s) (if any) that the function \( f \) is concave up? concave down? If there are any inflection points identify their points? Find \( \lim _{x \rightarrow \infty} f(x) \) and \( \lim _{x \rightarrow-\infty} f(x) \). Sketch the graph of \( f \).

\( e = \frac { 2 } { \theta + 1 } . \quad \frac { d e } { d \theta } = - \frac { 2 } { ( \theta + 1 ) ^ { 2 } } \)

1) Evaluate \( \int_{0}^{2}\left(x^{3}+3 x^{2}\right) d x \)

Determina la derivada de las siguientes funciones. 1.- Encuentra la derivada de la función \( f(x)=3 x+x^{2} \) 2.- Encuentra la derivada de la función \( f(x)=-2 x^{2}+5 \) 3.- Encuentra la derivada de la función \( f(x)=3 x \) 4.- Encuentra la derivada de la función \( f(x)=2 x-6 \) 5.- Encuentra la derivada de la función \( f(x)=x^{3} \)