Question

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

Answer 1

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.