Let f and g be the twice differentiable functions on R such that f''(x)=g''(x)+6x f'(1)=4g'(1)-3=9 f(2)=3g(2)=12. Then which of the following is NOT true?

(D) If -1 < x < 2, then |f(x)-g(x)| < 8

(B) There exists x₀ (1,3/2) such that f(x₀)=g(x₀)

(C) |f'(x)-g'(x)| < 6⇒ -1 < x < 1

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 29 Jan, Evening shift · Q3709

JEE Main 202329 Jan, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f

and

g

be the twice differentiable functions on

\mathbb{R}

such that

f''(x)=g''(x)+6x

f'(1)=4g'(1)-3=9

f(2)=3g(2)=12

. Then which of the following is NOT true?

JEE Main 2023 · 29 Jan, Evening shift · Q3709

JEE Main 202329 Jan, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f

and

g

be the twice differentiable functions on

\mathbb{R}

such that

f''(x)=g''(x)+6x

f'(1)=4g'(1)-3=9

f(2)=3g(2)=12

. Then which of the following is NOT true?