Question

you overhear the following statement \the number of people in poverty at the national level isnt decreasing as quickly as it used to.\ if n(t) gives the number at poverty level as a function of time, t, what can you conclude about the first and second derivatives of the function? n(t) is dropdown and n(t) is dropdown

Explanation:

Step1: Analyze First Derivative

The number of people in poverty \( N(t) \) is decreasing, so the first derivative \( N'(t) \) (rate of change) should be negative (since a decreasing function has a negative derivative).

Step2: Analyze Second Derivative

It's not decreasing as quickly as before, meaning the rate of decrease is slowing down. For a function with a negative first derivative, if the rate of decrease is slowing, the second derivative \( N''(t) \) (rate of change of the first derivative) is positive (because the first derivative is becoming less negative, i.e., increasing).

Answer:

\( N'(t) \) is negative and \( N''(t) \) is positive.