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Line tangent to the curve

by mbisCool
Tags: curve, line, tangent
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mbisCool
#1
Oct26-08, 04:40 PM
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1. The problem statement, all variables and given/known data

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


3. 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 im not mistaken but im 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!
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HallsofIvy
#2
Oct26-08, 05:03 PM
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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 im 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
#3
Oct26-08, 05:31 PM
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P: 136
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 :(


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