how to find maxima and minima?and plz suggest me some sums for it

 

If a function y= f(x) defined on (a,b)  is increasing in a particular interval say(a,c) . it remains stationery at x=c and decreases strictly in (c,b) . this shows that the function will have a max value at x=c and this value is called as a local maximum.

now for a function to have a local maximum at a particular point the conditions are i) the first derivative should be equal to 0

     ii) the second derivative should be < 0

similarly for a function to have a local minimum the conditions are:

     i) the first derivative should be = 0

     ii) the second derivative should be >0

 

there are many good problems given arihant series .try them.

here solve these,

1) John has x children by his first wife. mary has (x+1) children by her first husband. john and mary both marry and have children of their own . the whole family has 24 children. assuming that 2 children of the same family do not fight find the maximum possible number of fights in the family.

2) 2 roads OA and OB interesct at an angle 60 degrees . a car driver approaches O from Awhere AO =800m at  a uniform speed of 20m/s . simultaneously a jogger starts running from O toward s B at a uniform speed of 5m/s . find the time when the car and the runner are closest.