New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Differentiation question

2023 · 29 Jan · Shift 2 · Q38

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Differentiation
2023 · 29 Jan · Shift 2 · Q38

Differentiation question

2023 · 29 Jan · Shift 2 · Q38

JEE MainMathematicsDifferentiationMCQ+4 / −1

Let

f

and

g

be the twice differentiable functions on

\mathbb{R}

such that

f''(x)=g''(x)+6xf'(1)=4g'(1)-3=9f(2)=3g(2)=12

. Then which of the following is NOT true?

A
$g(-2)-f(-2)=20$
B
There exists $x_0\in(1,3/2)$ such that $f(x_0)=g(x_0)$
C
$|f'(x)-g'(x)| \lt 6\Rightarrow -1 \lt x \lt 1$
D
If $-1 \lt x \lt 2$ , then $|f(x)-g(x)| \lt 8$

More from Differentiation

Let $f^{1} (x) = \frac{3 x + 2}{2 x + 3}, x \in R - {\frac{- 3}{2}}$ For $n \geq 2$ , define $f^{n} (x) = f^{1} o f^{n - 1} (x)$ . If $f^{5} (x) = \frac{a x + b}{b x + a}, gcd (a, b) = 1$ …2023 · Numerical
Let $y = f (x) = sin^{3} (\frac{π}{3} (cos (\frac{π}{3 2} (- 4 x^{3} + 5 x^{2} + 1)^{\frac{3}{2}})))$ . Then, at x = 1,2023 · MCQ
If $y = tan^{- 1} (sec x^{3} - tan x^{3}), \frac{π}{2} < x^{3} < \frac{3 π}{2}$ , then2022 · MCQ
Let f : R $\to$ R be defined as $f (x) = x^{3} + x - 5$ . If g(x) is a function such that $f (g (x)) = x, \forall^{'} x^{'} \in R$ , then g'(63) is equal to .2022 · MCQ
The value of $lo g_{e} 2 \frac{d}{d x} (lo g_{c o s x} cosec x)$ at $x = \frac{π}{4}$ is2022 · MCQ
Let f : R $\to$ R satisfy $f (x + y) = 2^{x} f (y) + 4^{y} f (x)$ , $\forall$ x, y $\in$ R. If f(2) = 3, then $14. \frac{f ^{'} ( 4 )}{f ^{'} ( 2 )}$ is equal to .2022 · Numerical
For the curve $C : (x^{2} + y^{2} - 3) + (x^{2} - y^{2} - 1)^{5} = 0$ , the value of $3 y^{'} - y^{3} y^{''}$ , at the point $α > 0$ , $α > 0$ , on C, is equal to .2022 · Numerical
If $cos^{- 1} (\frac{y}{2}) = lo g_{e} (\frac{x}{5})^{5}, ∣ y ∣ < 2$ , then :2022 · MCQ