Question

If $f\left(x\right)=x^3$ and $g\left(x\right)=x^3-4x$ in $-2\le x\le 2$, then consider the statements:

(A) f(x) and g(x) satisfy 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.

• A. (A) and (B) are correct
• B. (A) alone is correct
• C. None is correct
• D. (A) and (C) are correct

Answer 1

The correct option is D

(A) and (C) are correct

$f(-2)\ne f\left(g\right),g(-2)=g\left(2\right)=0$