A function of two variables can have maxima, minima, saddle point or nothing. Two variable functions have 3-dimensional graphs and hence its maxima or minima will look like the peak of the bowl. Saddle point looks like the saddle in the back of the horse. For estimating the maxima and minima first we find the points at which these cases are possible and for that, we need to know the partial derivatives of the function. So, first of all, we will learn the partial derivatives of the function and then we will learn the working rule to find the maxima, minima, and the point of the saddle.
Partial Derivatives of the Multivariable Function
If we have the multivariable function, we can differentiate it with respect to one variable at a time keeping other variables constants and this is called as the partial derivative of a function with respect to a particular variable. We can differentiate the function multiple times with respect to a particular variable keeping other variables constant and this is called the multiple derivatives of the function. Watch the video lecture to understand the partial derivative concept.
Maxima and Minima of fuction of two variables
To find the maxima and minima of the function, first, we differentiate it with respect to both the variables ( say x and y) independently and equate it to zero. In the second step, we solve the simultaneous equations in x
That is all for this section, repeat the video to grasp the concept and ask your doubts and we will answer them ASAP.