a) Estimate the intervals on which the derivative is positive and the intervals
ID: 2875773 • Letter: A
Question
a) Estimate the intervals on which the derivative is positive and the intervals on which the derivative is negative.
Enter your answers in increasing order to one decimal place.
The derivative is positive on the intervals ___________________ < t < ____________________ and __________________ < t < ____________________.
The derivative is negative on the intervals ___________________ < t < ____________________ and __________________ < t < ____________________.
b) Estimate the intervals on which the second derivative is positive and the intervals on which the second derivative is negative.
Enter your answers in increasing order to one decimal place.
The second derivative is postive on the intervals _____________________ < t < ___________________.
The second derivative is negative on the intervals ___________________ < t < ___________________ and ______________________ < t < _________________.
Explanation / Answer
Derivative is positive ==> the function is increasing
In the given graph the function is increasing in the interval (0 , 1) and (2.7 , 7)
Hence derivative is positive for 0 < t < 1 and 2.7 < t < 7
Derivative is negative ==> the function is decreasing
In the given graph the function is decreasing in the interval (1 , 2.7) and (7 , 8)
Hence derivative is negative for 1 < t < 2.7 and 7 < t < 8
second derivative is positive ==> the function is concave up in the interval
The function is concave up in the interval (2 , 5)
Hence second derivative is positive in the interval 2 < t < 5
second derivative is negative ==> the function is concave down in the interval
The function is concave down in the interval (1 , 2) and (5 , 8)
Hence second derivative is negative in the interval 1 < t < 2 and 5 < t < 8
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