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The graph shows how the average age of first marriage of Japanese men varied in the last half of the 20th century. Sketch the graph of the derivative function $ M'(t) $. During which years was the derivative negative?

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It appears that there are horizontal tangents on the graph of $M$ for $t=1963$ and $t=1971 .$ Thus, there are zeros for those values of $t$ on the graph of $M^{\prime}$, The derivative is negative for the years 1963 to 1971.

02:46

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Marymargaret P.

September 28, 2020

The graph of f is given. State the numbers at which f is not differentiable. x = (smaller value) x = (larger value)

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04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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So in this problem were given a graph of the average age of first marriage of japanese men From 1960 to 2000 and were asked to sketch the graph of the derivative function in prime of T. And which years was the derivative negative? Well, since this is m right in the graph of the derivative is the slope of this curve. Okay, so we can first see that this slope over here at the beginning in this area is roughly one, right? It's roughly a slope of one happening there. Well, what do we see? We see the slope is positive but it's going towards zero because when we get to hear the slope is zero. So we're here, it's zero. Okay, so our slope might go something like this. Okay then this is a decreasing curve. So that's a negative slope. And again, right here we're at a slope of zero again, aren't we? So we have some decreasing curve down here. Okay, then what happens then? We start to take off with some positive slope. But you notice it like levels out as we're going across here. Right, so the slope kind of heads back towards zero. So the slope goes up to some Positive number and then heads back towards zero as we move out through there. Okay, so there's our curve paragraph. This would be 1970 and 1960 would be over here and so on, 1980 here, roughly. Okay, and so on. So when is it negative? Well, we're at a negative velocity during this time frame right here From like 1960 two or 3. Somewhere in there, Maybe 1963, 1970. A derivative negative, Right? Less than zero. Okay, there we go.

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