Question

computer video games can be delivered in one of two formats: digital (downloaded from a site) or physical (such as a dvd). the graph shows the thousands of games delivered in physical format since 2004 from the company supersoft. notice a downward surge occurred when digital formats first became more affordable and available. complete parts a through b below. a is f (2008) positive or negative? a. positive b. negative what does the sign of f (2008) mean to supersoft? in 2008 the number of games delivered in physical format was decreasing. b use the graph to compare f (2008) and f (2013). choose the correct answer below. a. the absolute value of f (2013) is less than the absolute value of f (2008). b. the absolute value of f (2008) is less than the absolute value of f (2013).

Explanation:

Step1: Understand the derivative meaning

The derivative $f'(x)$ represents the rate - of - change of the function $f(x)$. If the function is decreasing, the derivative is negative; if increasing, positive.

Step2: Analyze the graph at $x = 2008$

The graph of the number of games delivered in physical format is decreasing in 2008. So $f'(2008)<0$, and the answer to part a is negative.

Step3: Analyze the steepness of the graph at 2008 and 2013

The steepness of the graph represents the magnitude of the derivative. The graph is steeper in 2008 than in 2013. A steeper graph means a larger magnitude of the derivative. So, $|f'(2013)|<|f'(2008)|$.

Answer:

a. B. negative
b. A. The absolute value of $f'(2013)$ is less than the absolute value of $f'(2008)$