Question

find all of the x values for which f(x) = x^5 and g(x) = x^4 have tangent lines which are parallel. What are the equations for the two tangent lines?

Answer 1

what is the requirement for two lines to be parallel?

Answer 2

there isn't any more information to that question

Answer 3

Well that's because it is information you should know before calculus, maybe like 7th grade material.

Answer 4

So run a google search and tell me the requirements for two lines to be deemed parallel, then come back and we can do the rest

Answer 5

oh lol do you mean like same slope?

Answer 6

Yea, that is what I mean, so now. How do you find the slope of the tangent line of a function?

Answer 7

find the derivative

Answer 8

Right, so you can find derivatives yea?

Answer 9

Then, we know that in order to be parallel, our slopes must be equal, so set the derivatives equal and get your x values.

Answer 10

then do some 8th grade point slope stuff and you got it

Answer 11

ok so when i set the two equal to each other i got x = 4/5

Answer 12

I'm betting there are two answers

Answer 13

but, lemme run it in wolfram 1 sec

Answer 14

yep, there are two. 4/5 is one

Answer 15

and zero

Answer 16

yep, now just find the lines that contain those points and find the slopes and make the lines