Question

If $m$ is the slope of a tangent to the curve $e^{2y}=1+4x^2$ then

• A. $|m|<1$
• B. $|m|\ge 1$
• C. $|m|>1$
• D. $|m|\le 1$

Answer 1

The correct option is D

$|m|\le 1$

Taking $\log$ on both the sides, we get

$2y=\text{log}(1+4x^2)$

Differentiating with respect to $x$, we get

$2\frac{dy}{dx}=\frac{8x}{1+4x^2}$

$\Rightarrow \frac{dy}{dx}=\frac{4x}{1+4x^2}$

Since, $4x\le 1+4x^2$ so $|m|\le 1$