PREVIOUS ANSWERS 14. [0/1 Points] DETAILS MY NOTES ASK YOUR TEACHER SCALCET9 14.6.066. PRACTICE ANOTHER At what points does the normal line through the point (1, 2, 1) on the ellipsoid 4x + y + 4z = 12 intersect the sphere x+ y+z2 = 486? smaller x-value (x, y, z) = larger x-value (x, y, z) = Need Help? Read It Viewing Saved Work Revert to Last Response Submit Answer 8. [-/1 Points] DETAILS SCALCET9 14.7.044.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Let d be the distance from a point on the plane x 2y + 3z = 9 to the point (0, 2, 1). For f(x, y) = d, find the following derivatives. - fx(x, y) = Fy(x, y) = Find the critical point. (x, y) = Find the point on the plane x (x, y, z) = Need Help? Read It - 2y3z9 that is closest to the point (0, 2, 1). Consider the following. f(x, y) = Find Vf(x, y). X 2x -(3-3) Vf(x, y) = Determine Vf(x, y) at the point P = (3, -1). VF(3,-1) = (1,6) Determine a unit vector in the direction of PQ where P = (3, 1) and Q = (-6, 11). u = 6157 157 11157 157 Find the directional derivative of the function at the point P in the direction of the point Q. x) = -1 P(3, 1), Q(-6, 11) f(x, y) = Need Help? Read It 8. [-/1 Points] DETAILS SCALCET9 14.6.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 7xy, (3, -7) maximum rate of change direction vector Need Help? Read It 9. [1/1 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER SCALCET9 14.6.035.MI. PRACTICE ANOTHER Find all points at which the direction of fastest change of the function f(x, y) = an equation.) y=x+1 Need Help? Read It Watch It Master It 10. [0/1 Points] DETAILS + y-6x8y is i + j. (Enter your answer as PREVIOUS ANSWERS SCALCET9 14.6.038. PRACTICE ANOTHER MY NOTES ASK YOUR TEACHER The temperature at a point (x, y, z) is given by T(x, y, z) = 100e 3y - 7z where T is measured in C and x, y, z in meters. (a) Find the rate of change of temperature (in C/m) at the point P(2, -1, 3) in the direction toward the point (5, -3, 4). C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P. + calcPad Operations Functions Symbols Relations Sets O! Vectors Trig 5. [0.28/1 Points] DETAILS PREVIOUS ANSWERS MY NOTES ASK YOUR TEACHER Consider the following function. f(x, y) = x + y + xy + 8 Find the following derivatives. fx(x, y) = 2xy + 2x fy(x, y) = x+2y Find the critical point. (x, y) = 0,0 Find the value of f at this critical point. 8 SCALCET9 14.7.035.EP.DEFECTIVE PRACTICE ANOTHER Find the minimum and maximum of f on each segment of the boundary. minimum y = -1 9 x = 1 y = 1 x = -1 maximum 9 Find the absolute maximum and minimum values of f on the set D. D = {(x, y) | |x| 1, y 1} absolute maximum value absolute minimum value Need Help? Watch It Viewing Saved Work Revert to Last Response PREVIOUS ANSWERS 6. [0/1 Points] DETAILS MY NOTES ASK YOUR TEACHER SCALCET9 14.7.040. PRACTICE ANOTHER Find the absolute maximum and minimum values of f on the set D. f(x, y) = x-3x - y + 12y + 2, D is quadrilateral whose vertices are (-2, 3), (2, 3), (2, 2), and (-2, 2) absolute maximum value 67 absolute minimum value -22 Need Help? Read It