How do you find the Slope of the curve ##y=sqrt(x)## at the point where ##x=4##?

The slope of the curve ##y=f(x)## at ##x=a## is ##f'(a)##. Let us look at the posted problem.

By rewriting the square-root as 1/2-power, ##f(x)=sqrt{x}=x^{1/2}##

By the power rule, ##f'(x)=frac{1}{2}x^{ -1/2}=frac{1}{2sqrt{x}}##

By plugging in ##x=4##, Slope: ##m=f'(4)=frac{1}{2sqrt{4}}=frac{1}{4}##

Hence, the slope is ##1/4##.

I hope that this helps.