10) For this problem use f(x,y)= (-1/12x^3) +xy+ (1/8y^2)

(a) Find the first partial derivatives fx and fy

fx= (blank)

fy= (blank)

(b)Find all critical points of f. Show your work, but also put your final answer at the bottom of the page

Critical Point(s) (x and y coordinates): (Blank)

(c) Find the second partial derivatives

fxx=(Blank)

fxy=(Blank)

fyx=(Blank)

fyy= (Blank)

(d) Classify the critical point(s) according to the determinant test. Put your final answer(s) in the box, writing "None" if there are no answer(s) to write in the box. "none" if there are no answer(s) to write in the box.

relative max at (Blank); relative min at (Blank); saddle point at (Blank)

Please fill in the blanks with an explanation. Thank you!