Given function :
Now, we can check value of the function Z at (1,1), (1,5) , (4,1), (4,5)
So, Z is maximum at (4,1) and maximum value is 29/17. Similarly, Z is minimum at (1,5) and minimum value is 12/9.
The function Z has No local maxima or local minima in the interval ; except at the corner points of the interval.
To see this we can apply the method "Max/min for functions of two variables" which is a tedius task.
First we find partial derivatives w.r.t x and y.
∂f /∂x =
∂f /∂y =
A point (a, b) which is a maximum, minimum or saddle point is called a stationary point.
To find the stationary points of Z = f(x, y), work out ∂f /∂x and ∂f /∂y and set both to zero. This gives you two equations for two unknowns x and y. Solve these equations for x and y
So, to find stationary points, we put both equal to zero and find stationary points.
means x = 0 ; means y = 0
So, only stationary point possible is But at the function Z is Not defined, so, we can say that there is No stationary point for this function.