6. [-/3 Points] DETAILS SCALCET9 14.4.003.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following surface. z = 4x2 + y2 - 5y Let z = f(x, y). Find f (x, y) and f (x, y). fx ( x, y ) = fy ( x, y ) = Find an equation of the tangent plane to the given surface at the point (1, 2, -2). Need Help? Read it Submit Answer 7. [-/1 Points] DETAILS SCALCET9 14.4.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the tangent plane to the given surface at the specified point. z = x sin(y - x), (3, 3, 0) Need Help? Read it Watch It Submit Answer 8. [-/6 Points] DETAILS SCALCET9 14.4.020. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Explain why the function is differentiable at the given point. -2+y f(x, y) = 2 4 y' (1, 19) The partial derivatives are f (x, y) = and fy ( x , y ) = , so fy( 1, 19 ) = and fy(1, 19 ) = Both f and f, are continuous functions for ---Select-- , so f is differentiable at (1, 19). Find the linearization L(x, y) of the function at (1, 19). L( x, y) = Need Help? Read It Submit Answer 9. [-/1 Points] DETAILS SCALCET9 14.4.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Given that f is a differentiable function with f(4, 6) = 5, f (4, 6) = 1, and f (4, 6) = -1, use a linear approximation to estimate f(4.2, 5.9). f(4.2, 5.9) = Need Help? Read It Submit Answer 10. [-/2 Points] DETAILS SCALCET9 14.4.032. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the differential of the function. z = x In(y* + 5) dz= Jax + Need Help? Read It Submit Answer 11. [-/5 Points] DETAILS SCALCET9 14.5.003.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following. z = xy's - x2y, x = t2 + 1, y = +2 - 1 Find each of the following. ax oz av dx dt dy Use the chain rule to find z az dt