Question

How do you find the slope of the tangent line to the graph of the equation at the point with x-coordinate for `y = sqrt(x)` at p(4,2)?

Answer 1

You first find the derivative and then use that at `x_p=4`

Explanation:

`y=sqrtx=x^(1/2)->`

`y'=1/2 x^(-1/2)=1/(2*sqrtx)`

Using `x_p=4`:

`y'(4)=1/(2.sqrt4)=1/4`

And this is the slope.