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 $