Study23 2 years ago 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!

1. Algebraic!

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

2. Study23

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

3. Algebraic!

yes

4. Study23

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

5. Study23

Where do I proceed from here?

6. Algebraic!

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

7. Study23

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

8. Algebraic!

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

9. Algebraic!

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

10. Study23

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

11. Algebraic!

yes

12. Study23

ok thanks for the help!

13. Algebraic!

sure:)