Find an equation to the tangent line to the curve at the given point. (So, I have to find the derivative, but Im stuck - not sure if I am doing this correctly). Function is y=x^(5/2) Point is \(\ (4,32). Please show me step by step! I'm really confused!

Question

anonymous · Answer

you can do it the usual way.... (x^n) ' = nx^(n-1)

n is 5/2

anonymous · Answer

Okay, so that is the derivative....?

anonymous · Answer

yes

anonymous · Answer

I thought it was 5/2(x)^(3/2)

anonymous · Answer

Where do I proceed from here?

anonymous · Answer

plug in x=4 to find the slope (m) of the tangent to the curve at that point..
use y= mx +b   with the point they gave in order to find b

anonymous · Answer

Oh Okay. I was trying to plug the derivative in for m, but I guess that isn't correct.

anonymous · Answer

yeah, you just want the value of the derivative at that particular point...

anonymous · Answer

not the general expression for the slope at any value of x..

anonymous · Answer

So Is this the derivative?  5/2(x)^(3/2)

anonymous · Answer

yes

anonymous · Answer

ok thanks for the help!

anonymous · Answer

sure:)