SOLUTION: What is the slope of y^2=b^3/(2x+b) at (0,b)

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Question 1186078: What is the slope of y^2=b^3/(2x+b) at (0,b)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


y%5E2=b%5E3%2F%282x%2Bb%29
y%5E2=b%5E3%282x%2Bb%29%5E%28-1%29

Use implicit differentiation.

2y%28dy%2Fdx%29=-2b%5E3%282x%2Bb%29%5E%28-2%29

dy%2Fdx=%28-b%5E3%29%2F%28y%282x%2Bb%29%5E2%29

Evaluate the derivative at (x,y)=(0,b)

dy%2Fdx=%28-b%5E3%29%2F%28b%28b%5E2%29%29=%28-b%5E3%29%2Fb%5E3=-1

ANSWER: -1