Question

if we apply rolles theorem to the function (f(x) = 2x^2 - 16x - 1) on the interval (2, 6), how many values of (c) exist such that (f(c) = 0)?

what is the value of (c)?

if we try to apply rolles thorem to the function (f(x) = 2x^2 - 16x - 1) on the interval (-1, 13), which of the following conditions is not met?

(f(a) = f(b))
continuty on (-1, 13)
differentiability on (-1, 13)

Explanation:

Verify Rolle's Theorem conditions on [2, 6]

$$
LATEXBLOCK0
$$

Solve for c in (2, 6) where f'(c) = 0

$$
LATEXBLOCK1
$$

Evaluate Rolle's Theorem conditions on [-1, 13]

$$
LATEXBLOCK2
$$

Answer:

Question 1

1

Question 2

4

Question 3

• \(f(a) = f(b)\) (Correct answer)
• continuity on \([-1, 13]\)
• differentiability on \([-1, 13]\)