KCET2014MathematicsPermutation and Combination
If ( f(x)=x³ ) and ( g(x)=x³-4 x ) in ( -2 x 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
Options
- A(a) alone is cortect
- B(a) and (c) are correct.
- C(a) and (b) are correct.
- DNone is correct.
Correct answer
B. (a) and (c) are correct.
Step-by-step solution
Given that, f(x)=x³ and g(x)=x³-4 x Since, f(x) and g(x) are both continuous at [-2,2] and differentiable at [-2,2] So, f(x) and g(x) satisfy mean value theorem. Now, f(-2)=-8, f(2)=8 So, f(-2) f(2)g(2)=(2)³-4(2)=0=g(-2)=(-2)³-4(-2)=0 Therefore, f(x) does not satisfy Rolle's theorem but g(x) satisfy Rolle's theorem.