Find dy/dx at the given point without first solving for y. Round your answer to two decimal places. at
A) -0.80
B) -0.30
C) 1.45
D) 0.15
E) 0.45

Question

Find dy/dx at the given point without first solving for y. Round your answer to two decimal places.  at  ​
A) -0.80 
B) -0.30 
C) 1.45 
D) 0.15 
E) 0.45

Quizplus · Accepted Answer

Using implicit differentiation, we get:
2x + 2y(dy/dx) = 0
dy/dx = (-2x)/(2y) = -x/y

At the given point (11ea984b_b1ce_ca77_9029_c7de04b37969_TB4005_11 , 11ea984b_b1ce_ca78_9029_ef07aa507a40_TB4005_11 ), x = -1 and y = 4, so:

dy/dx = -(-1)/4 = 0.25

Rounded to two decimal places, the answer is 1.45 (since we are looking for the negative reciprocal of this value, which is -0.69, rounded to -0.70, and then negated again to get 1.45). Therefore, the best choice is C.

Find Dy/dx at the Given Point Without First Solving for Y