Question

Consider the curve $y=e^{2x}$.What is the slope of the tangent to the curve at (0, 1) ?

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

The correct option is C 2

We know that slope of tangent to a curve $y=f\left(x\right)$ at a point $(x_1,y_1)$ equals $f^{{}^{\prime }}\left(x_1\right)$

$\Rightarrow$ Slope of tangent to the curve $y=e^{2x}$ equals $\frac{d\left(e^{2x}\right)}{dx}=2e^{2x}$

$\Rightarrow$Slope of tangent at $(0,1)=f^{{}^{\prime }}\left(0\right)=2$