Applications Of Derivatives Question 420
Question: The slope of the tangent to the curve $ y=\sqrt{4-x^{2}} $ at the point where the ordinate and abscissa equal is
Options:
A) -1
B) 1
C) 0
D) none of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Here, y>0. Putting $ y=x $ in $ y=\sqrt{4-x} $ , we get $ x=\sqrt{2},-\sqrt{2.} $
So, the point is $ (\sqrt{2},\sqrt{2}) $ .
Differentiating $ y^{2}+x^{2}=4 $ w.r.t. x, we get $ 2y\frac{dy}{dx}+2x=0 $ Or $ \frac{dy}{dx}=-\frac{x}{y} $
$ \therefore At(\sqrt{2},\sqrt{2}),\frac{dy}{dx}=-1 $