Given $f ( x ) = x ^ { 2 } + 6 x$

question 154

Multiple Choice

Given $f ( x ) = x ^ { 2 } + 6 x$ .
(a) Find the intervals on which $f$ is increasing or decreasing.
(b) Find the relative maxima and relative minima of $f$ .

• A) (a) Increasing on \(( - 3 , \infty )\),
• decreasing on \(( - \infty , - 3 )\)
• (b) Rel. min. \(f ( - 3 ) = - 9\)
• B) (a) Increasing on \(( - \infty , - 3 )\),
• decreasing on \(( - 3 , \infty )\)
• (b) Rel. max. \(f ( - 3 ) = - 9\)
• C) (a) Increasing on \(( - 6 , \infty )\),
• decreasing on \(( - \infty , - 6 )\)
• (b) Rel. min. \(f ( - 6 ) = 0\)
• D) (a) Increasing on \(( - \infty , - 6 )\),
• decreasing on \(( - 6 , \infty )\)
• (b) Rel. max. \(f ( - 6 ) = 0\)

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Definitions:

Annual Dividends

The total amount of dividend payments made to shareholders over a year.

Market Value

Market value is the current price at which an asset or service can be bought or sold in an open market.

Retained Earnings

The portion of net income left over for a business after it has paid out dividends to its shareholders, often reinvested into the business.

Cumulative Net Income

The total profit of a company after all expenses and taxes have been deducted, accumulated over a period of time.