Write a formula for the distance between a point (x, y) on the graph of y = x4 and the point (4, 8). Express your answer in terms of x

Question

anonymous · Answer

The shortest distance between a point on this graph and a point somewhere else, will occur at a perpendicular to the graph.  Can you find the slope (as a function) of your function?

anonymous · Answer

slope is (8-y)/(4-x) right?

anonymous · Answer

That is a slope... are you in Calculus?

anonymous · Answer

yes thats what im asking you

anonymous · Answer

2nd day in calc

anonymous · Answer

Awesome... you can also find a slope with a derivative.  Ahhh, second day.  So this one is gonna be rough.

anonymous · Answer

ok so if i have the slope what do i do next?

anonymous · Answer

I made an equation for a line to start... but that is not going to help you.  
I would say that you would use a distance formula.$$\sqrt{(y _{2}-y _{1})^{2}+(x _{2}-x _{1})^{2}}$$

anonymous · Answer

y2 would be your function, x2 would just be x.
(x1,y1) is your point

anonymous · Answer

should i just make a distance formula for just point x,y and 4,8?
but what about x^4

anonymous · Answer

$$d(x)=\sqrt{(x ^{4}-8)^{2}+(x-4)^{2}}$$

anonymous · Answer

This way, the first point is (4, 8) and the second point is$$(x, x ^{4})$$

anonymous · Answer

oh i got it

anonymous · Answer

thank you so much babe

anonymous · Answer

I thought that it was a different question at first... sorry for the lag.  I had to get my bearings and start from the beginning. 
You're welcome.

anonymous · Answer

i know i was confuse because i was trying to find the slope and do a mx+b equation

anonymous · Answer

Lol! Yup that's what I did... der.

anonymous · Answer

can you help me with a new question? :)

anonymous · Answer

ok

anonymous · Answer

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