Question

What's the derivative of the function at the given point? `f(x)=1/x^(1/2)` ,at `(1/4,2)`

Answer 1

The derivative of the function at `x= 1/4` will be `(1/4, -4)`.

Explanation:

We can immediately write the function as

`f(x) = x^(-1/2)`

Then we can find the derivative using the power rule.

`f'(x) = -1/2x^(-3/2) = -1/(2x^(3/2))`

Now we have

`f'(1/4) = -1/(2(1/4)^(3/2)) = -1/(2(1/8)) = -1/(1/4) = -4`

Hopefully this helps!