Applications of Partial Differentiation and Successive Differentiation.
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See all →- What is a Jacobian of two or three variables and how do I calculate it? In one line The Jacobian J=∂(u,v)/∂(x,y) is the determinant of all first partial derivatives of u,v with respect to x,y ; it measures how a... 1
- What is Lagrange's method of undetermined multipliers for finding maxima and minima with a constraint? In one line To optimise f(x,y,z) subject to φ(x,y,z)=0 , form F=f+λφ and solve F_x=F_y=F_z=0 together with φ=0 . Explained simply Suppose yo... 1
- What are maxima and minima of a function of two variables and how do I find stationary points? In one line A function f(x,y) has a maximum (minimum) at a point if its value there is larger (smaller) than at all nearby points; such poin... 1
- How do I use the second derivative test with r, s, t to classify maxima, minima and saddle points? In one line At a stationary point compute r=f_xx , s=f_xy , t=f_yy : if rt-s²>0 it is a maximum when r<0 and a minimum when r>0 ; if rt-s²<0... 1
- What is a saddle point of a function of two variables and how do I identify it? In one line A saddle point is a stationary point that is a maximum along one direction and a minimum along another, so it is neither a maxim... 1
- How do I solve a word problem on maxima and minima, like the box with least surface area? In one line Write the quantity to optimise as a function, use the given condition to reduce it to two variables, then find and classify the... 1