Qual o gradiente da função f(x,y) = -x2 - y + 4 ?

f(x,y) = -x^2-y+4

Fx(x,y) = -2x - 0 - 0 = -2x

Fy(x,y) = - 0 - 1 - 0 = -1

(-2x , -1)

O gradiente da função é dado por:

\(G=\frac{\partial F}{\partial x},\frac{\partial F}{\partial y}\)

Assim:

\(\frac{\partial F}{\partial x}=-2x-0+0\\ \frac{\partial F}{\partial x}=-2x\)

e

\(\frac{\partial F}{\partial y}=0-1+0\\ \frac{\partial F}{\partial y}=-1\)

Portanto:

\(​​G=\frac{\partial F}{\partial x},\frac{\partial F}{\partial y}\\ G=-2x,-1\)

Alternativa B