help someone, please?! i dont want the answer, i want guidance. The expression dy/dx = x(3√y) gives the slope at any point on the graph of the function f(x) where f(2) = 8.

Question

anonymous · Answer

A. Write the equation of the tangent line to f(x) at point (2, 8).

what am i supposed to do? differentiate?

anonymous · Answer

@mathmale could you please help me?

anonymous · Answer

the equation came out wrong. it's supposed to look like this:
$$dy/dx=x(\sqrt[3]{y})$$

anonymous · Answer

what are the initial steps i should take?

anonymous · Answer

@AccessDenied are you going to help me?

accessdenied · Answer

One note:  y = f(x).  Because dy/dx = the slope of f(x) at a point.

We want to find the equation for a tangent line.
So, we want two pieces of information:
   The point, which is given:  (2, 8)
   The slope at that point, which we use dy/dx = x cuberoot(y)   and our point to find.

anonymous · Answer

@agent0smith help please?

accessdenied · Answer

We can plug in our point information into the formula for dy/dx, which will give us the slope at the point.
Then we use point-slope formula to get the equation of the line:
  y - y0 = m(x - x0)     (x0, y0) = (2, 8).   m = dy/dx(2,8)

anonymous · Answer

so do we just plug in the point into the equation then make an equation?

anonymous · Answer

i got it! i think...
would the equation of the tangent line be y=4x?

accessdenied · Answer

That looks good!  :)

accessdenied · Answer

Sorry the site had a moment and I went to do some other things in the mean time;  I missed the updates!

anonymous · Answer

it's okay. i solved it! thanks a million!

accessdenied · Answer

Glad to help!