Applications-Of-Derivatives Question 456

Question: If normal to the curve $ y=f(x) $ is parallel to x-axis, then correct statement is

[RPET 2000]

Options:

A) $ \frac{dy}{dx}=0 $

B) $ \frac{dy}{dx}=1 $

C) $ \frac{dx}{dy}=0 $

D) None of these

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Answer:

Correct Answer: C

Solution:

Slope of the normal = $ -\frac{1}{( \frac{dy}{dx} )} $ This is parallel to x-axis Þ $ -\frac{1}{( \frac{dy}{dx} )}=0 $ Þ $ \frac{dx}{dy}=0 $ .