This Question: 1 pt 10 of 18 (17 complete) Find the directions in which the function...
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in those directions u f(x,y,z) = 4 In (xy) + 2 In (yz)+2 In (xz). Po(1,1,1) In which direction does the function increase most rapidly? (i+1+O (Type exact answers, using radicals as needed) In which direction does the function decrease most rapidly? = (1+) ;+ OK (Type exact answers, using radicals as needed.) What is the value of the...
Find the directions in which the function increases and decreases most rapidly at Po Then find the derivatives of the function in these directions f(x,y,z) = (x/y) - yz, Po(-3.1.4) The direction in which the given function f(x,y,z) = (x/Y)- yz increases most rapidly at Po(-3.1.4) isu = 11+( 1+ k (Type exact answers, using radicals as needed) The direction in which the given function f(x,y,z) = (x/y) - yz decreases most rapidly at Po(-3.1.4) is -u=1:-( k (Type exact...
Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. xy) =x"cos(y) +x"win(x) cos(x)sin(y). Plo The direction in which the given function txy_f(xy)-x3cos(v)+x2vsin(x) + cos(x)sin(y)increases most rapidly at P 0주 is u: " (Type exact answers, using radicals as n (xy)=x3cos(y)+x"win(x)-cos(x)sin(y) The direc on in which the given function f(xy- is eases most rapidly at (Type exact answers, using radicals as needed The derivative of the...
Find the directions in the xy-plane in which the function fixy) 15-2x2 -y2 has zero change at the point P(2,1,3) Express the directions in terms of unit vectors What is the unt vector in a direction of zero change with a positive x-component? Type exact answers, using radicals as needed.) What is the other unit vector in a direction of zero change? (Type exact anowers, using radicals as needed.) cess Ubrary Enter your answer in each of the answer boxes...
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
please show all the steps 15.5.37 Question Help A function f and a point P are given. Let θ correspond to the direction of the directional derivative. Complete parts (a) through (e) #x,y)-10-4x2-3y2, P(3,4) a. Find the gradient and evaluate it at P The gradient at P is b Find the angles θ with respect to the positive x-axis associated with the directions of maximum increase, maximum decrease, and zero change What angle(s) is/are associated with the direction of maximum...
9. Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = x² Inx²+3 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on and increasing on (Simplify your answers. Use a comma to separate answers as needed. Type your answers in interval notation. Type exact answers, using radicals as needed.) OB. The function is decreasing on . The...
9. Find the intervals on which fis increasing and the intervals on which it is decreasing. f(x) = x? In x² +3 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on and increasing on (Simplify your answers. Use a comma to separate answers as needed. Type your answers in interval notation. Type: exact answers, using radicals as needed.) OB. The function is decreasing on The...
26. For the function f(x,y) = 4y2 + 3x², find f(3. - 4), (-4,4), f(-1,-2), and f(0,7). f(3,-4)= (Type an exact answer, using radicals as needed.) f(-4,4)= (Type an exact answer, using radicals as needed.) f(-1, - 2) = (Type an exact answer, using radicals as needed.) f(0.7) = (Type an exact answer, using radicals as needed.)
The position of a particle in space at time is r(t) as shown below. Find the particle's velocity and acceleration vectors. Then find the particle's speed and direction of motion alt=1 (0 (4 in (t+1) The particle's velocity is 1.3k Clype exact answers, using radicals as needed.) The particle's acceleration is +3.0k (Type exact answers, using radicals as needed) The particle's speed at t=1s (Type an exact answer, using radicals as needed) The particle's direction at t=1s (+0+* (Type exact...