a function f(x,y) increases most rapidly at a point (x0,y0) in the direction of gradf(x0,y0) and decreases most rapidly in the direction of -gradf(x0,y0)

gradf(x,y) = <fx , fy> = <12(y^2)(x^2) , 8(x^3)y>

gradf(2,1) = <48 , 64>

so -gradf(2,1) = <-48, -64>

u = <-48, -64>/(sqrt(48^2 + 64^2)) = <-48/80 , -64/80> = <-3/5 , -4/5> ....unit vector in the direction of most rapid decrease

the rate of change in the direction of u is given byb) what is the rate of change of f in the direction given in (a).

|-gradf(2,1)| = 80