For the simple harmonic motion equation d = 8 cos (pi/2t), what is the maximum displacement from the equilibrium position?

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