Determine slope of the tangent at the given value,
c. $f(x)=\sqrt{x+1}, a=0$

Answer

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Answer

The slope of the tangent line to the function $f(x)=\sqrt{x+1}$ at $x=0$ is $\boxed{\frac{1}{2}}$.

Steps

Step 1 ：Let's find the derivative of the function $f(x)=\sqrt{x+1}$.

Step 2 ：The derivative of $f(x)=\sqrt{x+1}$ is $f'(x)=\frac{1}{2\sqrt{x+1}}$.

Step 3 ：Substitute $x=0$ into the derivative to find the slope of the tangent line at $x=0$.

Step 4 ：The slope of the tangent line to the function $f(x)=\sqrt{x+1}$ at $x=0$ is $\boxed{\frac{1}{2}}$.