 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, find the local maxima and local minima if any of the following functions. Find also the local maximum and local minimum values as the case may be. fx is equal to x square. First of all let us understand that if we are given a function f defined on open interval i, then let function f be continuous at a critical point c in interval i. Then if f dash x is greater than 0 for x less than c and if f dash x is less than 0 for x greater than c then c is the point of local maxima. Now let us discuss when c is the point of local minima if f dash x is less than 0 for x less than c and f dash x is greater than 0 for x greater than c then c is the point of local minima. This is the key idea to solve the given question. Now let us start the solution. We are given function f given by fx equal to x square. Now differentiating both sides with respect to x we get f dash x equal to 2x. Now to find the points of maxima and minima we will put f dash x equal to 0. So we can write 2x is equal to 0. This implies x is equal to 0 so we get critical point as 0. Now when x is less than 0 then f dash x is also less than 0 and when x is greater than 0 then f dash x is also greater than 0. Now clearly we can see f dash x changes its sign from negative to positive as x increases through 0. So this implies x equal to 0 is the point of local minima. Now let us find out local minimum value. You know local minimum value is equal to f0. f0 is equal to 0 square. Now we can simply write it as 0. So we get local minimum value equal to 0. So our required answer is function f has local minima at x equal to 0 and local minimum value is equal to 0. This completes the session. Hope you understood the session. Bye.