Let f(x,y)= x^2y^3-x+y^2-50
1. Find fy: (3x^4)(y^2) -0 + 2y - 0 = (3x^4)(y^2)+2y
Do I add the remaining power of y to x?
2. Find f yx i.e (fy)x: What exactly does this represent? Do I take fy of the previous example, when we solved for fx? The answer would be 6x^4y+2
3. Find the slope of the tangent line to the curve of intersection of the graph of f(x,y) and the plane x=3 at the point where x=3 and y=2. I start by plugging in (3,2) into fx= (3x^4)(y^2)+2y which gives me (3(3)^4) (2^2)+2(2)= 328 which leads me to believe I made an error in finding fx.
4. Find a vector parallel to the tangent line in #3
1i+0j+328k
5. Find the parametric equations of the tangent line in #3
x-3=1t
y-2=0t
z-0=328t
1. Find fy: (3x^4)(y^2) -0 + 2y - 0 = (3x^4)(y^2)+2y
Do I add the remaining power of y to x?
2. Find f yx i.e (fy)x: What exactly does this represent? Do I take fy of the previous example, when we solved for fx? The answer would be 6x^4y+2
3. Find the slope of the tangent line to the curve of intersection of the graph of f(x,y) and the plane x=3 at the point where x=3 and y=2. I start by plugging in (3,2) into fx= (3x^4)(y^2)+2y which gives me (3(3)^4) (2^2)+2(2)= 328 which leads me to believe I made an error in finding fx.
4. Find a vector parallel to the tangent line in #3
1i+0j+328k
5. Find the parametric equations of the tangent line in #3
x-3=1t
y-2=0t
z-0=328t