To calculate: The derivative of the function
Answer to Problem 19E
The derivative of the function is
The behavior of the function is interpreted as, the function first increases reaches the maximum at
Explanation of Solution
Given information:
The function
Formula used:
The slope of a function at a given point is the derivative of the function at that point.
Product rule of
Calculation:
Consider the function
Differentiate the function with respect to z ,
Recall product rule of differentiation
Apply it,
Therefore, derivative of the function of the function is
Recall that the slope of a function at a given point is the derivative of the function at that point.
Evaluate the value of the function and slope at the points
At the point
Substitute
Substitute
At the point
Substitute
Substitute
At the point
Substitute
Substitute
The graph of the function is provided below,
The behavior of the function is interpreted as, the functionfirst increases reaches the maximum at
Thus, derivative of the function is
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Chapter 2 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
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