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(1)if p and k be real numbers such that x^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 of f(x,y)=x^2+y^2 – xy,where x and y are connected by the relation x^2+4y^2 =4 are?

(1)if p and k be real numbers such that
x^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 of
f(x,y)=x^2+y^2 – xy,where x and y are connected by the relation x^2+4y^2 =4 are?

Grade:12

2 Answers

Ravi
askIITians Faculty 69 Points
9 years ago
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.
vineet chatterjee
42 Points
9 years ago
sir,it would be very kind of you if you please post the answers,i have tried in the same way,please post the answers sir,please.................................................................................

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