Question

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

• A. $(0,2)$
• B. $(2,0)$
• C. $(-\frac{1}{2},0)$
• D. $noneofthese$

Answer 1

The correct option is C $(-\frac{1}{2},0)$

Slope of tangent $=\frac{dy}{dx}=e^{2x}\times 2=e^o\times 2=2$ at $(0,1)$

$\Rightarrow$ Tangent passes $(0,1)$ and has slope $2$

$\Rightarrow$ Equation $y-1=2(x-0)$

$\Rightarrow y=2x+1$

It meets x-axis, $(y=0)$ at $x=-\frac{1}{2}$