To calculate: The first and second derivative of the function
Answer to Problem 25E
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.
Power rule of differentiation,
Calculation:
Consider the provided function
Evaluate the first derivative of the function,.
Apply sum rule of differentiation,
Apply the power rule of differentiation,
Evaluate the second derivative of the function, differentiate the first derivative again with respect to x .
Apply the power 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
The point where the graph changes it nature is known as the point of inflection.
To sketch the graph of the function
Observe that first derivative of the function
Now, first derivative can be both negative and positive depending on values of x ,
First derivative will be negative if,
Therefore, the function
First derivative will be positive if,
Therefore, the function
Next observe that second derivative of the function
At
Therefore, the graph of the function
Thus, the value of first derivative of the function is
Want to see more full solutions like this?
Chapter 2 Solutions
Modeling the Dynamics of Life: Calculus and Probability for Life Scientists
- Determine whether each of the following statements is true or false, and explain why. The derivative of a sum is the sum of the derivatives.arrow_forwardFind the derivative of each function defined as follows. y=5x4+9x3+12x2-7xarrow_forwardDetermine whether each of the following statements is true or false, and explain why. The derivative of 10x is x10x-1.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,