If $f(x) = x^3$ and $g(x) = x^3 - 4x$ for $-2 \leq x \leq 2$, then consider the statements: (a) $f(x)$ and $g(x)$ satisfy the Mean Value Theorem. (b) $f(x)$ and $g(x)$ both satisfy Rolle's Theorem. (c) Only $g(x)$ satisfies Rolle's Theorem. Of these statements, which are correct?

Question

If $f(x) = x^3$ and $g(x) = x^3 - 4x$ for $-2 \leq x \leq 2$, then consider the statements:
(a) $f(x)$ and $g(x)$ satisfy the Mean Value Theorem.
(b) $f(x)$ and $g(x)$ both satisfy Rolle's Theorem.
(c) Only $g(x)$ satisfies Rolle's Theorem.
Of these statements, which are correct?

(a) alone is correct.

(a) and (c) are correct.

(a) and (b) are correct.

None are correct.

Solution

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