Question

If $f^{\prime \prime }\left(x\right)+f‘\left(x\right)+f^2\left(x\right)=x^2$ be differential equation of a curve and let P be the point of maxima, then the number of tangents which can be drawn from P to $x^2-y^2=a^2$ is/ are

• A. 1
• B. 2
• C. either 1 or 2

Answer 1

The correct option is B 2

For maxima f’(x) = 0 & f''(x) < 0
$\Rightarrow f^{\prime \prime }\left(x\right)=x^2-f^2\left(x\right)\le 0$
$\Rightarrow$ Point ‘P’ lies outside $x^2-y^2=a^2$