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

1 Answer
Oct 21, 2017

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!