In an episode of The Simpsons television show Homer Simpson

In an episode of The Simpsons television show, Homer Simpson reads from a newspaper and announces, “Here’s good news! According to this eye-catching article, SAT scores are declining at a slower rate.” Interpret Homer’s statement in terms of a function and its first and second derivative.

Solution

Let the function f(x) represents the SAT scores of particular year x

Since SAT scores are declining as per Homers statement, hence f(x) is decreasing we define the first derivative as

f\'(x) = [f(a+h) - f(a)]/(a+h-a)

Since f(a+h) < f(a), since the function is decreasing, hence the first derivative of the function will be negative

The second derivative of the function will be positive