Given f(x, y) = x^2y^3 - x + y^2 - 50
1. Find fy (partial deriv)
My answer: fy = (x^2)(3y^2) + (2y)
2. Find fyx
My answer: fyx = 2x3(y^2) = 6x(y^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.
My answer:
. . .(3, 2, 23)
. . .(3^2)(2^3) - 3 + (2^2) - 50
. . .9*8 - 3 + 4 - 50 = 23
. . .(3^2)*(3*(2^2) + (2*2)
. . .9*12 + 4 = 112
4. Find a vector parallel to the tangent line in #3.
My answer: 0i + 3j + 112k
5. Find the parametric equations of the tangent line in #3.
My answer:
. . .(x - 3) = ot
. . .(y - 2) = 3t
. . .(z - 23) = 112t
Is this correct for #3,4,5?
1. Find fy (partial deriv)
My answer: fy = (x^2)(3y^2) + (2y)
2. Find fyx
My answer: fyx = 2x3(y^2) = 6x(y^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.
My answer:
. . .(3, 2, 23)
. . .(3^2)(2^3) - 3 + (2^2) - 50
. . .9*8 - 3 + 4 - 50 = 23
. . .(3^2)*(3*(2^2) + (2*2)
. . .9*12 + 4 = 112
4. Find a vector parallel to the tangent line in #3.
My answer: 0i + 3j + 112k
5. Find the parametric equations of the tangent line in #3.
My answer:
. . .(x - 3) = ot
. . .(y - 2) = 3t
. . .(z - 23) = 112t
Is this correct for #3,4,5?
