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3.4 Concavity

3.4 Concavity. Concavity. Let f be differentiable on the open interval I. f is concave up on I if f’ is increasing on I and concave down on I if f’ is decreasing on I. Concavity Test. F is a function whose 2 nd derivative exists on an open interval I

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3.4 Concavity

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  1. 3.4 Concavity

  2. Concavity • Let f be differentiable on the open interval I. f is concave up on I if f’ is increasing on I and concave down on I if f’ is decreasing on I.

  3. Concavity Test • F is a function whose 2nd derivative exists on an open interval I • 1. if f”(x)>0 for all x in I then f is concave up • 2.if f”(x)<0 for all x in I then f is concave down

  4. Determining concavity intervals • Determine the open intervals on where it is concave up or down.

  5. Answer • Take 2nd derivative and test • Concave up: (-∞,0) • Concave down: (0,∞)

  6. Determining concavity intervals • Determine the open intervals on where it is concave up or down.

  7. Answer I • Take 2nd derivative and test

  8. Answer II • Test and conclude • Concave up: (-1,∞)

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