To calculate: The first and second derivative of the function
Answer to Problem 22E
The value of first derivative of the function is
Explanation of Solution
Given information:
The function
Formula used:
Let a function g be continuous on closed interval
If first derivative of the function is greater than zero that is
If first derivative of the function is less than zero that is
If second derivative of the function is greater than zero that is
If second derivative of the function is less than zero that is
The point where the graph changes it nature is known as the point of inflection.
Quotient rule of differentiation,
Calculation:
Consider the provided function
Evaluate the first derivative of the function, apply the quotient rule of differentiation,
Evaluate the second derivative of the function, differentiate the first derivative again with respect to x .
Apply the quotient rule of differentiation,
Recall if first derivative of the function is greater than zero that is
If first derivative of the function is less than zero that is
If second derivative of the function is greater than zero that is
If second derivative of the function is less than zero that is
To sketch the graph of the function
Observe that first derivative of the function
Next observe that second derivative of the function
Therefore, the graph of the function
Thus, the value of first derivative of the function is
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