Describe how the graph of \( g(x)=\sqrt[3]{x}-5 \) can be obtained from the graph of \( f(x)=\sqrt[V]{x} \). Then graph the function \( g(x) \). How can the graph of \( g(x)=\sqrt[3]{x}-5 \) be obtained from the graph of \( f(x)=\sqrt[3]{x} \) ? A. Shift the graph 5 units left. B. Shift the graph 5 units down. C. Shift the graph 5 units up. D. Shift the graph 5 units right.

Let \( f(x)=2 x^{3}+9 x^{2}-60 x+3 \) a. Find all points on the graph of \( f(x) \) at which the tangent line is horizontal. b. Find all points on the graph of \( f(x) \) at which the tangent line has slope -36

8. \( \int \frac{7}{x^{4} d x} \)

Um capital de \( R \$ 600,00 \), aplicado à taxa de juros simples de \( 30 \% \) ao ano, gerou u montante de \( R \$ 1320,00 \) depois de certo tempo. O tempo de aplicação foi de: l,69

Solve the equation or formula for the variable indicated. \( 7 f+g=5 \), for \( f \)

Let \( C(x) \) represent the cost of producing \( x \) items and \( p(x) \) be the sale price per item if \( x \) items are sold. The profit \( P(x) \) of selling \( x \) items is \( P(x)=x p(x)-C(x) \) (revenue minus costs). The average profit per ltem when \( x \) items are sold is \( P(x) / x \) and the marginal profit is \( d P / d x \). The marginal profit approximates the profit obtained by selling one more item given that \( x \) items have already been sold. Consider the following cost functions \( C \) and price functions \( p \). Complete parts (a) through ( \( d \) ) below \( C(x)=-0.03 x^{2}+60 x+120, p(x)=200, a=500 \) Anterpret the marginal profit if \( x=a \) units have been sold Choose the correct answer below A. The profit per item for each of the first 500 items produced is \( \$ 154.76 \) B. The profit for the 170 items produced is \( \$ 50000 \) C. The profit for the 501 st item produced is \( \$ 170.00 \) D. The marginal profit for the first 500 items produced is \( \$ 154.76 \)