(1)if p and k be real numbers such thatx^3 – px^2+kx-6=0 has its roots real and positive,then the minimum value of k is? (2)the maximum value of f(x)=sin(x)+cos(x) when x lies between [0,2pie] is? (3)the least and greatest value off(x,y)=x^2+y^2 – xy,where x and y are connected by the relation x^2+4y^2 =4 are?

2.Use AOD, 2nd order derivative method to find the solution of the eqn in the forst and third quadrant for maximum and minimum value of the function.

3. Substitute the value of x or y(here taken x) from x^2+4y^2 =4 in tof(x,y)=x^2+y^2 – xy.

Diffrentiate f(x) and eqaute to zero to obtain 2 solutions(each corresponding to maxima and minima). Find f’’(x) and put both the values to know the value of x resulting in maxima or minima.