6. [-/8 Points] DETAILS I LARCALCET713.6.046. I MYNOTES II ASKYOURTEACHER I Consider the following. f(x, y) = 9x2 + 4y2 6 = 52, P(2, 2) (3) Find the gradient of the function at P. (b) Find a unit vector that is normal to the level curve f(X, y) = C at P. (c) Find the tangent line to the level curve f(x, y) = c at P. (d) Sketch the evel curve, the unit normal vector, and the tangent line in the xyplane. O O Show My Work (Required) @ What steps or reasoning did you use? Your work counts towards your score_ Uploaded File (10 le maximum) You can submit show my work an unlimited number of times. No Files to Display v) Upload File 9. [-/3 Points] DETAILS LARCALCET7 13.5.036.MI. MY NOTES ASK YOUR TEACHER Differentiate implicitly to find the first partial derivatives of w. x2 + y2 + z2 - 3yw+ 6w2 = 9 aw ax aw ay aw az 10. [-/2 Points] DETAILS LARCALCET7 13.5.012. MY NOTES ASK YOUR TEACHER Consider the following. w = xy2 + x2z+ yz2, x = th, y = 6t, z =6 (a) Find dw/dt using the appropriate Chain Rule. . = dt (b) Find dw/dt by converting w to a function of t before differentiating. dw dt7. [-/2 Points] DETAILS LARCALCET7 13.6.058. MY NOTES ASK YOUR TEACHER The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and y are measured in centimeters. Find the direction from point P where the temperature increases most rapidly. T ( x, y) = 35 - x2 - 5y2, P(1, - 2) Find the rate of increase. (Round your answer to two decimal places.) o per centimeter 8. [-/8 Points] DETAILS LARCALCET7 13.5.016. MY NOTES ASK YOUR TEACHER Find aw/as and Ow/at using the appropriate Chain Rule. Function Values w = y3 - 5x2y x = es, y = et S = -4, t = 8 aw as ow at Evaluate each partial derivative at the given values of s and t. aw as at Show My Work (Required) ? What steps or reasoning did you use? Your work counts towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display Upload File Show My Work has not been graded yet.1. {-11 Points] DETAILS LARCALC10 13.6.002. MY NOTES ASK YOUR TEACHER Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the unit vector u = cos 6i + sin Bj. f(X. y) = y. P(2, 0), 9 = % 5X+y 2. [-I1 Points] DETAILS LARCALC10 13.6.006. MY NOTES ASK YOUR TEACHER Find the directional derivative of the function at P in the direction of v. \\/_ f(X. y) = X3 - y3, PM, 3), v = _2 (i + j) i: 2 3. [l1 Points] DETAILS LARCALC10 13.6.022. MY NOTES ASK YOUR TEACHER Find the directional derivative of the function at P in the direction of v. f(X,y,z)=xy+yz+xz, P(3,4,3), v=6i+jk I: 4. {-11 Points] DETAILS LARCALCET7 13.6.026.MI. MY NOTES ASK YOUR TEACHER . Use the gradient to find the directional derivative of the function at P in the direction of PQ. f(X, y) = 3x2 y2 + 4, P0, 1). 0(2. 2) I: 5. [-I2 Points] DETAILS LARCALCET7 13.6.035. MY NOTES ASK YOUR TEACHER Find the gradient of the function at the given point. Function Point RX. y, 2): VX2+y2+z2 (5,912) Vf(5, 9, 2) = Find the maximum value of the directional derivative at the given point. D