Question

The point where the tangent line to the curve $y=e^{2x}$ at $(0,1)$ meets $x$ - axis is -

• A. $(1,0)$
• B. $(-1,0)$
• C. $(-\frac{1}{2},0)$
• D. None of these

Answer 1

Answer: (C)

$(-\frac{1}{2},0)$

$y=e^{2x}$
$\frac{dy}{dx}=e^{2x}\times 2$
$\therefore {\left(\frac{dy}{dx}\right)}_{(0,1)}=2$
Thus equation of tangent at point $(0,1)$ is, $y-1=2(x-0)\Rightarrow y=2x+1$
Now substitute $y=0$ to get point of intersection of tangent with $x-axis$
$x=-\frac{1}{2}$
Therefore, required point is $(-\frac{1}{2},0)$
Hence, option 'C' is correct.