Advanced MathHardEndpoint from a given average rate
Advanced Math practice question
For the function f(x) = x², the average rate of change of f between x = 1 and x = c (with c > 1) is 9. What is the value of c?
Answer: 8
The average rate is (c² − 1)/(c − 1) = c + 1. Setting c + 1 = 9 gives c = 8.
Common wrong answers
- If you answered 9
- 9 is the average rate itself; c satisfies c + 1 = 9.
- If you answered 10
- The simplified rate is c + 1, so c = 9 − 1 = 8.
- If you answered 80
- Factor c² − 1 = (c − 1)(c + 1) before dividing — the quotient is just c + 1.
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