Homework Soursefor the function fxyx34x2yy2 and point p01 and Q33 iwhat is
for the function f(x,y)=x^3-4x^2y+y^2 and point p(0,1) and Q(3,3) (i)what is the gradient vector delta f of f. (ii)what is delta f at point p.(iii)find the rate of change of f in direction from p to Q. (iv)and what is maximum rate of change of f at p ,the diraction in which it occure.
Solution
i)df/dx = 3 x^2 - 8 xy - 4 x^2 dy/dx +2y dy/dx as x and y are independent variables df/dx = 3 x^2 - 8 xy ii) at point p df/dx= 0 iii) df/dx|at q - df/dx|at p df/dx|at q = -45 df/dx|at p = 0 df/dx|at q - df/dx|at p = -45 iv) maximum rate of change of f at p d(df/dx)/dx = 6 x -8x dy/dx - 8y = 0 dy/dx = 6x - 8y /8x dy/dx = infinity which is the direction parallel to y axis.
