the complete question in the attached figure
a) gradient vector for this function
f(x,y)-------- > 2x² -y² +3x-y
it is necessary to calculate two partial derivatives
d f(x,y)/d (x)=4x+3
d f(x,y)/d (y)=-2y-1
∀f(x,y) (gradient vector) ------------------- >(4x+3)i+(-2y-1)j
the answer part a) is (4x+3)i+(-2y-1)j
b) The direction of the line passing through the point (1,-2) having the maximum slope
insert x=1 and y=-2 into the gradient vector function
∀f(x,y) (gradient vector) ------------------- >(4*1+3)i+(-2*(-2)-1)j
∀f(x,y)=(7)i+(3)j
the answer part b) is (71+3j)
c) The magnitude of the slope at point (1,-2)
║V║=√(7² +3²)=√58=7.62
the answer part c) is 7.62