The graph of a function fis shown below. Graph Graph Description lnteractive 3D Graph @- Help 2 G) Find an equation of the tangent plane to the surface 2 = f(x, y) at the specified point. f(x, 3/) = 15 X2 y2 x+y=4 X Find the linear approximation of the function f(x, y, z) = \l X2 + y2 + 22 at (2, 4, 4) and use it to approximate the number V 2.012 + 3.982 + 3.972. (Round your answer to five decimal pieces. ) F(2.01, 3.98, 3.97) 2 {31.72000 x The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasing as the resistor heats up. Use Ohm's Law,V = IR, to find how the current I is changing at the moment when R = 383 Q, I = 0.06 A, dV/dt = 0.03 V/s, and dR/dt = 0.05 (1/5. (Round your answer to six decimal places.) :A/s (a) Show that a differentiable function fdecreases most rapidly at x in the direction opposite the gradient vector, that is, in the direction of Vf(x). Let 9 be the angle between Vf(x) enc unit vector 11. Then Duf= |Vf_ y . Since the minimum value of_ y is y occurring, for O S H X (c) What is the maximum rate of change at P? X Find the local maximum and minimum values and saddle point(s) oi' the function. You are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) f(X, y) =)(3 + y3 3X2 6y2 9)( local maximum value(s) 5 / local minimum value(s) '59 / saddle point(s) (X! Y) = DNE Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) flxr Y) = V2 - 6y c0500, 4 s x s 4 local maximum value(s) DNE / local minimum value(s) 9 / saddle point(s) (X, y) = DNE