finding the slope of a tangent line

• Sep 16th 2012, 11:41 AM
neontiger94
finding the slope of a tangent line
I have been stuck on this question for a while now. I need to find the slope of the tangent to the curve 5 over the square root of x (5/squarerootX)
• Sep 16th 2012, 11:49 AM
skeeter
Re: finding the slope of a tangent line
start by rewriting $\displaystyle y = \frac{5}{\sqrt{x}}$ so that you may use the power rule for derivatives

$\displaystyle y = 5x^{-1/2}$

continue ...
• Sep 16th 2012, 12:08 PM
neontiger94
Re: finding the slope of a tangent line
When I use the power rule I get (-5/2) (x^-3/2) if i did that right i am still going to have a radical so how will I find the slope?
I'm sorry for coming off as such an amateur, but calc is the bane of my existence
• Sep 16th 2012, 12:36 PM
Plato
Re: finding the slope of a tangent line
Quote:

Originally Posted by neontiger94
When I use the power rule I get (-5/2) (x^-3/2) if i did that right i am still going to have a radical so how will I find the slope?
I'm sorry for coming off as such an amateur, but calc is the bane of my existence

You don't. The tangent at $\displaystyle \left(x_0,\frac{5}{\sqrt{x_0}}\right)$ is $\displaystyle y-\frac{5}{\sqrt{x_0}}=\frac{-5}{2\sqrt{x_0^3}}(x-x_0)$
• Sep 16th 2012, 12:40 PM
neontiger94
Re: finding the slope of a tangent line
Thats what I thought the answer was, but maybe I didnt specify the question properly. The question reads Find the slope m of the tangent to the curve
y = 5/square root x

at the point where x = a > 0.
does this help at all, beacuse I think I'm supposed to find the exact slope using the derivative as a function
• Sep 16th 2012, 12:47 PM
Plato
Re: finding the slope of a tangent line
Quote:

Originally Posted by neontiger94
Thats what I thought the answer was, but maybe I didnt specify the question properly. The question reads Find the slope m of the tangent to the curve
y = 5/square root x at the point where x = a > 0.
does this help at all, beacuse I think I'm supposed to find the exact slope using the derivative as a function

Always post the complete problem.

But that changes nothing in what I posted. Just let $\displaystyle a=x_0$ and you are done.
• Sep 16th 2012, 01:01 PM
neontiger94
Re: finding the slope of a tangent line
Okay thank you I should have used the power rule from the beginning