Question

5 mark for review
the table gives characteristics of the rates of change of the function f on different intervals. which of the following is true about f on the interval 3 < x < 4?

x	1 < x < 2	2 < x < 3	3 < x < 4	4 < x < 5

Explanation:

Step1: Analyze the given table

The table shows the rate - of - change characteristics of the function \(f(x)\) on different intervals. For the interval \(3 < x<4\), it is stated that the rate of change of \(f(x)\) is positive and decreasing.

Step2: Recall the relationship between rate of change and the function

A positive rate of change of a function \(y = f(x)\) means that the function is increasing (since \(\frac{\Delta y}{\Delta x}>0\)). A decreasing rate of change means that the slope of the tangent line to the function is getting less steep (but still positive) as \(x\) increases in the interval \(3 < x<4\). So the function \(f(x)\) is increasing at a decreasing rate on the interval \(3 < x<4\).

Answer:

The function \(f(x)\) is increasing at a decreasing rate on the interval \(3 < x<4\).