Simple Calculus I Question

[SilentButDeadly]

Question:

Show that the curve y=6x^3+5x-3 has no tangent line with slope 4.

Known:

Well of course we know that the y' is 18x^2+5, so since x=sqrt(-5/18), would that prove that the curve has no tangent line because x has an imaginary number?

or

Would you set the derivative equal to 4? ---- 4=18x^2+5
This would still give you an imaginary number, x=sqrt(-1/18). Would this be the proof?

or

Am I just totally off here? I am not to sure. I kind of think that the second thing I did would show why there is no tangent lin on the curve, but I am not to sure.

Would someone mind helping me out on this problem. It is simple I know, but I think I may be thinking to much in it or something. I appreciate the help in advance 🙂

 

[Sam334]

Originally posted by: SilentButDeadly
Question:

Show that the curve y=6x^3+5x-3 has no tangent line with slope 4.

Known:

Well of course we know that the y' is 18x^2+5, so since x=sqrt(-5/18), would that prove that the curve has no tangent line because x has an imaginary number?

or

Would you set the derivative equal to 4? ---- 4=18x^2+5
This would still give you an imaginary number, x=sqrt(-1/18). Would this be the proof?

or

Am I just totally off here? I am not to sure. I kind of think that the second thing I did would show why there is no tangent lin on the curve, but I am not to sure.

Would someone mind helping me out on this problem. It is simple I know, but I think I may be thinking to much in it or something. I appreciate the help in advance 🙂

I believe that's your answer.

 

[StevenYoo]

2nd one methinks.

slope = derivative.

so if y' != 4, then u've proved it.

 

[vrbaba]

Originally posted by: Sam334

Originally posted by: SilentButDeadly
Question:

Show that the curve y=6x^3+5x-3 has no tangent line with slope 4.

Known:

Well of course we know that the y' is 18x^2+5, so since x=sqrt(-5/18), would that prove that the curve has no tangent line because x has an imaginary number?

or

Would you set the derivative equal to 4? ---- 4=18x^2+5
This would still give you an imaginary number, x=sqrt(-1/18). Would this be the proof?

or

Am I just totally off here? I am not to sure. I kind of think that the second thing I did would show why there is no tangent lin on the curve, but I am not to sure.

Would someone mind helping me out on this problem. It is simple I know, but I think I may be thinking to much in it or something. I appreciate the help in advance 🙂

I believe that's your answer.

YUP!

Both ways are Ok, but the "formal proof" would be to set it equal to 4, since that is what is being asked for.

 

[SilentButDeadly]

Cool, that is what I was thinking, just wasn't to positive. I appreciate the help! 🙂

 

[Oil]

Originally posted by: StevenYoo
slope = derivative.

QFT