Finding Tangent Line to a Curve at a Given Point

[mbisCool]

Homework Statement

For what values of a and b is the line 3x+y=b tangent to the curve y=ax^3 when x=5 ?

The Attempt at a Solution

I believe i would need to find the equation of the tangent to y=ax^3 when x=5 then that should be equal to -3x+b=y if I am not mistaken but I am not sure what to do from here to solve for a and b.

Any leads in the right direction or insight if this is the entirely wrong approach would be greatly appreciated!

 

[HallsofIvy]

I believe i would need to find the equation of the tangent to y=ax^3 when x=5 then that should be equal to -3x+b=y if I am not mistaken

Well, yes, that's just a restatement of the problem! You know that the slope of y= -3x+ b is -3. What connection is there between the slope of a tangent line and the function itself?

 

[mbisCool]

thank you for the quick reply hallsofivy. I had -0.04 instead of -3/75 giving me the wrong answer for the online homework webpage which was confusing me. After using -3/75 instead it counts it as correct :(