Question

Use the given graph of f to estimate the intervals on which the derivative f ' is increasing or decreasing. (Enter your answers using interval notation.)

Answer 1

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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