3. Consider the function 𝑓(𝑥) = −|𝑥 + 2| + 3

Question

a. Precisely state the Rolle’s Theorem.

b. For the given function, state the values of 𝑓(−8) and 𝑓(4).

c. A friend of yours claims that due to Rolle’s Theorem there should exist a value of c in the interval −8 < 𝑐 < 4 such that 𝑓 ′ (𝑐) = 0. Is your friend correct? Find such a c or explain why it does not exist.

Answer 1

The function is NOT differential at x=-2, so the theorem does not apply