Question

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

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

Answer 1

The correct option is C $(2,0)$

solution - equation of curve is y=$e^{2x}$

tangent to the curve is

$\frac{dy}{dx}=2e^{2x}$

$(\frac{d{e}^x}{dx}=e^x)$

At points (0,1), the tangent is

$(\frac{dy}{dx}{)}_{(0,1)}=2e^{2\left(0\right)}$

$(\frac{dy}{dx}{)}_{(0,1)}=2e^0$ $[e^0=1]$

${\frac{dy}{dx}}_{0,1}=2$

when the slope is 2, and solve the tangent

meets y axis the coordinate is 0,

Hence the tangent meets the x axis at (2,0)