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← Tangent Lines - Differential Equations in Action

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. Here we have two pretty simple exponential functions. Two to the power of X and three to the power of X.
  2. Two to the power of zero is one; three to the power of zero is one; two to the power of one is two.
  3. Two to the power of two is four. Two to the power of minus one equals one over two, one half, and so on.
  4. Three to the power of one equals three. Three to the power of two gets pretty big--nine.
  5. Three to the power of minus one, one over three, one-third, and so on, and so on.
  6. Here comes a quiz for you: What's the slope of the tangent line at X equals zero?
  7. Is the slope larger than one? Is it equal to one, or is it smaller than one?
  8. In both cases, look at the tangent lines--what would you say?