The derivative of a function is used to determine whether the function is increasing or decreasing on any intervals in its domain.
Derivative of function f is increasing in interval (-2 , 1) and (3 , 6)
Derivative of function f is decreasing in interval (1 , 3) and (6 , 9)
If f′(x) > 0 at each point in an interval , then the function is said to be increasing in that interval.
If f′(x) < 0 at each point in an interval , then the function is said to be decreasing on that interval.
By observing graph, it is observed that slope of function f is positive in interval (-2 , 1) and (3 , 6) . Hence, derivative of function f is increasing in interval (-2 , 1) and (3 , 6)
By observing graph, it is observed that slope of function f is negative in interval (1 , 3) and (6 , 9) . Hence, derivative of function f is decreasing in interval (1 , 3) and (6 , 9).
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