Applications Of Derivatives Question 378

Question: The number that exceeds its square by the greatest amount is

[Roorkee 1990]

Options:

A) - 1

B) 0

C) $ \frac{1}{2} $

D) 1

Show Answer

Answer:

Correct Answer: C

Solution:

Let the number is x, then $ y=x-x^{2} $

therefore $ \frac{dy}{dx}=1-2x $ and $ \frac{d^{2}y}{dx^{2}}=-2(<0) $

therefore $ 1-2x=0\Rightarrow x=\frac{1}{2} $ .