anonymous
  • anonymous
For what values of a and b is the line −4x+y=b tangent to the curve y=ax^3 when x=3?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
find the slope of each at 3 and the b value that makes them have the same y values at 3
anonymous
  • anonymous
y = 4x + b has a slope of 4 and y = ax^3 has a slope of ...
anonymous
  • anonymous
3a ?

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anonymous
  • anonymous
close, 3ax^2, and when x = 3, that equals...
anonymous
  • anonymous
so the slope is 3ax^2 even thou y=mx+b m being the slope?
anonymous
  • anonymous
Evaluate 3ax^2, where x = 3 to get 3a(3)^2 = 27a 27a is the slope at x = 3, and it has to equal 4 to be tangent to the line, so solve 27a = 4 to find a, then work on b the same way you would for an intersection of two functions.

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