#### To determine

**To sketch:** The graph of M′(t) and find the time in which the derivative is negative.

#### Answer

The derivative was negative in between the years 1963 and 1971.

#### Explanation

**Given:**

The given graph highlights the variation of the average age of first marriage of Japanese men varied in the last half of the 20th century.

**Calculation:**

From the graph, it is clear that the slope of the graph is positive initially.

The graph has horizontal tangent just after t=1960, after which the slope becomes negative.

After t=1970, it has horizontal tangent and then the slope becomes positive.

After t=2000, the slope becomes horizontal gradually.

This implies that, the derivative graph will positive initially with functional value zero just after t=1960, then the derivative graph will negative and then again the derivative will be zero just after t=1970.

After this, the derivative will be positive and after t=2000, the derivative becomes zero gradually.

**Graph:**

Use the above information to draw graph of M′(t) as shown below in Figure 1.

From Figure 1, it is observed that the derivative was negative when t∈(1963,1971).