00:01
In this question, the graph of f -dash -x is given and we need to answer the following questions.
00:08
First question is, on what interval this f -x is increasing? so we can say that f -x is increasing when f -dash -x is greater than 0.
00:23
And f -d -dash -x is greater than 0 means it is above the x -axis.
00:27
So f -x is greater than above x -axis in the interval when x -belongs to 0 -2.
00:34
To 2 0 to 2 union then after that 4 to 6 from 4 to 6 and then from 8 to 9 8 to 9 so basically in this interval fx is increasing in the second part b part it is being asked on the interval fx is decreasing or this question is asked in a part itself and it is decreasing when f -dash is less than 0 so f -dash is less than 0 when this graph is below than x -axis so at that interval is 2 to 4 from 2 to 4 union 6 to 8 this will be the interval when the graph is decreasing f x is decreasing now in the next part it is being asked in the second part that is b at what values of x does f have local maximum so if it is having local maximum we can we know that at local maximum f -dash x changes its sign from positive to negative at local maximum it changes that sign from positive to negative now we can see that at this point at two it is before two it is positive after two it is negative so basically x is equals to two will be the local maxima then and from at 4 it is becoming from negative to positive.
02:25
So it is not the point of local maximum.
02:27
Then again at 6 it is becoming from positive to negative.
02:31
So 2 .6 are the points of local maximum.
02:36
And then point of local minimum, as we know that at local minimum, f -dash -x changes its sign from negative to positive, negative to positive.
02:57
So we will just look at those values in which the sign is changing from negative to positive.
03:02
So graph is coming from negative to positive at 4 and at 8...