Question

Find the slope of the tangent to the curve $y=2\sqrt{x}$ at the point $(2,1)$.

• A. $\frac{1}{\sqrt{5}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\sqrt{3}$
• D. $\sqrt{5}$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

$y=2\sqrt{x}$
$\frac{dy}{dx}=2\left(\frac{1}{\left(2\surd x\right)}\right)=\frac{1}{\sqrt{x}}$
$\frac{dy}{dx}$ is called slope of the tangent to the curve $y=2\sqrt{x}$ at the point $(x,y)$.

For the point $x=2$ and $y=1$. Putting $x=2$ and $y=1$ in the equation $\frac{dy}{dx}=\frac{1}{\sqrt{x}}$ , we get $\frac{dy}{dx}=\frac{1}{\sqrt{2}}$.
Hence slope is $\frac{1}{\sqrt{2}}$.