What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
9. What is the instantaneous rate of change of 2 = f(x,y) = x + xy (with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2) ? e) none of these V13 12 -8 V13 13
(5 points) For the function y = 5x2: (a) Find the average rate of change of y with respect to x over the interval [5,7). (b) Find the instantaneous rate of change of y with respect to x at the value x = 5. Average Rate of Change: | Instantaneous Rate of Change at x = 5: (5 points) Let f(x) = 3x + 3x + 2 Use the limit definition of the derivative to calculate the derivative off: f'(x)...
Which one of the following is a linear transformation? O F(x, y) = xy O F(x,y) = (22,32) O F(x, y, z) = (x,y – 2,0) O F(x, y, z) = (2,4 – 2,1)
(r-2)2+2(y-1 )2 -2 +(y-1)for(x, y) (2,1) f(, y) for (a, y)(2, 1) 0 DNE lim а) Еxplain xy->(2,1) b)FubiniTheorem R =-1, 2] x-2, 21? (r-2)2+2(y-1 )2 -2 +(y-1)for(x, y) (2,1) f(, y) for (a, y)(2, 1) 0 DNE lim а) Еxplain xy->(2,1) b)FubiniTheorem R =-1, 2] x-2, 21?
13. Use the differential df at(5,2) to approximate the change in f(x,y) = x² + 3xy’as x increases from 5 to 5.01 and y decreases from 2 to 1.98. a)-976288 b)-980000 c)-983400 d)-990000 e) none of these
True or False? 1. If f(x) sin x then the average rate of change of f on the interval (1, ) is - 2. If g(x) = 5x – 7 then the average rate of change of g on 13, 317] is 5.
Find the average rate of change of f(x)=3x^2-2, from 2 to 4.
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
4) Compute the average rate of change of f(x) = -2 x² + 3x - 1 over the interval (-2, 6). Clearly present the formula being used to compute the average rate of change.