use implicit differentiation to find y’ and then evaluate y’ at (-1, -7). 8xy + y - 49 = 0 y’ = -8y / (8x +…
use implicit differentiation to find y’ and then evaluate y’ at (-1, -7). 8xy + y - 49 = 0 y’ = -8y / (8x + 1) y’|(-1, -7) = (simplify your answer.)
Answer
Explanation:
Step1: Substitute x and y values
Substitute $x = - 1$ and $y=-7$ into $y'=\frac{-8y}{8x + 1}$.
Step2: Calculate the numerator
The numerator is $-8y=-8\times(-7)=56$.
Step3: Calculate the denominator
The denominator is $8x + 1=8\times(-1)+1=-8 + 1=-7$.
Step4: Calculate y' value
$y'=\frac{56}{-7}=-8$.
Answer:
$-8$