I have not yet had the privilege of studying multivariable calculus, but I have made an educated guess about how to find the minimum or maximum of a function with two variables, for example, x and y.Since, in three dimensions, a minimum or maximum would be represented by a tangent plane with no slope in any direction, could I treat y as a constant and differentiate z with respect to x, then treat x as a constant and differentiate with respect to y, and find the places where both of these two are equal to zero?Sorry if this is just a stupid assumption... it may be one of those things that just seems correct but is actually wrong.

Question

I have not yet had the privilege of studying multivariable calculus, but I have made an educated guess about how to find the minimum or maximum of a function with two variables, for example,   x and   y.Since, in three dimensions, a minimum or maximum would be represented by a tangent plane with no slope in any direction, could I treat   y as a constant and differentiate   z with respect to   x, then treat   x as a constant and differentiate with respect to   y, and find the places where both of these two are equal to zero?Sorry if this is just a stupid assumption... it may be one of those things that just seems correct but is actually wrong.

aushilfem8sif · Accepted Answer

In fact you got quite a good &quot;guess&quot;. When it comes to finding maxima and minima of a function   f  :            R        2    →      R  , you begin by finding the critical points which, as you said, are obtained by solving the system:      {                                        f            x            ′                    (                      x            0                    ,                      y            0                    )          =          0                                                  f            y            ′                    (                      x            0                    ,                      y            0                    )          =          0                        The solution(s),   (      x    0    ,      y    0    ), is either going to be maxima, minima or saddlepoint. You determine which one it is by studying the Hessian matrix evaluated at that point.I&#039;m sure you will get to it when you start doing multivariable calculus. Great guess, however!

I have not yet had the privilege of studying multivariable calculus, but I have made an educated gue

Answered question

Answer & Explanation

New Questions in High school geometry