Recall equation (1)
Obtain the first derivative dW/dt by differentiating the equation on both sides, i.e.
In relation to the graph W vs t given by (1), dW/dt at a t-value will give the slope of the tangent at that t-value. What will be the slope of the tangent at the point where a graph has a minimum? Of course, it is zero (if you are not sure about this, review the section on slope). Therefore, in (2), if we make
Now, by solving (3), we can find the t-value
At this juncture, let us pause for a minute. Do we know for sure that this t-value corresponds to the minimum value of W? No, we do not! This t-value may very well correspond to the maximum value for W, because the slope of the tangent at the point where a graph has a maximum is also zero!!
For the case study presented in this lesson, show that the t-value in (4) corresponds to a minimum.
So, the minimum weight will occur 6.5 days after the baby is born and that minimum weight will be
This means that the baby will start to grow after 6 and a 1/2 days from birth.
Question: Could we have found this result without using the concept "derivative"? The answer is yes. See how with the derivative-free and algebraic approaches.