The function \( f(x) \) is defined below. What is the end behavior of \( f(x) \) ? \( f(x)=-14 x^{3}-7 x^{4}+56 x^{2}+126 x+63 \) Answer as \( x \rightarrow \infty, y \rightarrow-\infty \) and as \( x \rightarrow-\infty, y \rightarrow-\infty \) as \( x \rightarrow \infty, y \rightarrow \infty \) and, as \( x \rightarrow-\infty, y \rightarrow \infty \) as \( x \rightarrow \infty, y \rightarrow-\infty \) and as \( x \rightarrow-\infty, y \rightarrow \infty \) as \( x \rightarrow \infty, y \rightarrow \infty \) and as \( x \rightarrow-\infty, f, y \rightarrow-\infty \)

Suppose \( \int_{2}^{4} f(x) d x=6, \int_{2}^{7} f(x) d x=-2 \), and \( \int_{2}^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{7}^{7} 5 g(x) d x=20 \) 2 (Simplify your answer.) \( \int_{7}^{7}[g(x)-f(x)] d x=\square \) 2 (Simplify your answer.)

\( \int_{2}^{7} 5 g(x) d x=\square \) (Simplify your answer.)

Suppose \( \int^{4} f(x) d x=6, \int^{7} f(x) d x=-2 \), and \( \int^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{2}^{7} 5 g(x) d x=20 \) 2 (Simplify your answer.) 7 \( \int_{2}[g(x)-f(x)] d x=6 \) 2 (Simplify your answer.) 7 \( \int_{2}[5 g(x)-f(x)] d x=\square \) (Simplify your answer.)

Suppose \( \int_{2}^{4} f(x) d x=6, \int_{2}^{7} f(x) d x=-2 \), and \( \int_{2}^{7} g(x) d x=4 \). Evaluate the following integrals. \( \int_{7}^{2} g(x) d x=-4 \) (Simplify your answer.) \( \int_{7}^{7} 5 g(x) d x=20 \) 2 (Simplify your answer.) \( \int_{2}^{7}[g(x)-f(x)] d x=\square \) 2 (Simplify your answer.)

The president of a company that manufactures toy cars thinks that the function \( P(c)=-2 c^{2}+14 c-20 \) represents the company's profit, where \( c \) is the number of cars produced, in thousands, and \( P(c) \) is the company's profit, in hundreds of thousands of dollars. Determine the maximum profit the company can earn.