The Mean Value Theorem Worksheet with Answer Key

What's on the worksheet

1. Show that each function satisfies the three hypotheses of Rolle's theorem on the interval, giving the reason for each, and find every c the theorem…
   g(x) = x^3 - 6x^2 + 8x on [0, 4]h(x) = x\sqrt{9 - x^2} on [0, 3]
2. Decide whether the mean value theorem applies to the function on the interval.
   g(x) = x\ln x on [1, e]k(x) = \sqrt[3]{x} on [-1, 8]
3. Find the value of the constant k for which $f
4. Jin claims that $F
5. Let $p
6. Isabel swims one length of a 50-meter pool to the far wall, turns there, and swims back.
7. For each function, decide whether the theorem named applies on the interval.