Questions: Find the slope of the line tangent to the graph of f(x) = 2 sqrt(x) at x = 1/1.

Transcript text: Find the slope of the line tangent to the graph of $f(x)=2 \sqrt{x}$ at $x=\frac{1}{1}$. Answer: $\square$

Solution

Solution Steps

To find the slope of the tangent line to the graph of a function at a given point, we need to compute the derivative of the function and then evaluate it at the specified point. The derivative of a function gives us the slope of the tangent line at any point on the graph.

Step 1: Define the Function

The function given is $ f(x) = 2\sqrt{x} $.

Step 2: Compute the Derivative

To find the slope of the tangent line, we need the derivative of $ f(x) $. The derivative is: \[ f'(x) = \frac{d}{dx}[2\sqrt{x}] = \frac{1}{\sqrt{x}} \]

Step 3: Evaluate the Derivative at $ x = 1 $

Substitute $ x = 1 $ into the derivative to find the slope of the tangent line at this point: \[ f'(1) = \frac{1}{\sqrt{1}} = 1 \]