What is the average rate of change of the function f(x) = 17x² over the interval from 1 to 5?

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To find the average rate of change of the function f(x) = 17x² over the interval from 1 to 5, we use the formula for the average rate of change, which is:

Average Rate of Change = (f(b) – f(a)) / (b – a)

In this case, a = 1 and b = 5.

Now, we need to calculate f(1) and f(5).

Step 1: Calculate f(1)

Plugging x = 1 into the function:

f(1) = 17(1)² = 17(1) = 17

Step 2: Calculate f(5)

Now plug x = 5 into the function:

f(5) = 17(5)² = 17(25) = 425

Step 3: Substitute values into the average rate of change formula

Now we have:

  • f(1) = 17
  • f(5) = 425
  • a = 1
  • b = 5

Substituting these values into the average rate of change formula:

Average Rate of Change = (425 - 17) / (5 - 1) = 408 / 4 = 102

Conclusion

The average rate of change of the function f(x) = 17x² over the interval from 1 to 5 is 102.

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