Let $f$ be a function that is continuous and differentiable for all real $x$. If $f(2) = -4$ and $f'(x) \geq 6$ for all $x \in [2, 4]$,then which of the following is true?

  • A
    $f(4) < 8$
  • B
    $f(4) \geq 8$
  • C
    $f(4) \geq 12$
  • D
    None of these

Explore More

Similar Questions

If $f(x) = x^{\alpha} \log x, x > 0, f(0) = 0$ and $f(x)$ satisfies Rolle's theorem on $[0, 1]$,then what is the value of $\alpha$?

Difficult
View Solution

If $f(x)$ is differentiable on the interval $[2, 5]$ such that $f(2) = 1/5$ and $f(5) = 1/2$,then there exists a number $c$ such that $2 < c < 5$ and $f'(c) = \dots$

Difficult
View Solution

Values of $c$ as per Rolle's theorem for $f(x)=\sin x+\cos x+6$ on $[0, 2\pi]$ are

$A$ value of $c$ according to the Lagrange's mean value theorem for $f(x)=(x-1)(x-2)(x-3)$ in $[0,4]$ is

Consider the function $f(x) = \begin{cases} x \sin \frac{\pi}{x} & \text{for } x > 0 \\ 0 & \text{for } x = 0 \end{cases}$. Then the number of points in $(0, 1)$ where the derivative $f'(x)$ vanishes is:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo