Question

The average rate of change of g(x) between x = 4 and x = 7 is Five-sixths. Which statement must be true?

Answer 1

There are multiple statements that could be true, depending on the properties of g(x). Here are some possibilities:

- g(7) - g(4) = 5/6
- g(x) is a linear function
- The slope of the tangent line to g(x) at x = 5.5 is 5/6
- The derivative of g(x) at x = 5.5 is 5/6
- The graph of g(x) is concave up on the interval [4, 7]
- The graph of g(x) has a local maximum at x = 5.5 and a local minimum at x = 6.5.