Moira uses a difference quotient to determine the average rate of change of f(x) = x2 + 14x from x = –11 to x = 8. She shows the following work.

9514 1404 393

  (d) She substituted incorrectly ..

Step-by-step explanation:

The interval Moira wants to use to find the difference quotient is [-11, 8]. This is the interval [x, x+h], so ...

  x = -11

  x +h = 8

Then ...

  h = 8 -x = 8 -(-11) = 19

The proper substitution would be ...

  difference quotient = 2x +14 +h = 2(-11) +14 +19

  difference quotient = 11

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