Home
Class 12
MATHS
Given that f is a real valued differenti...

Given that f is a real valued differentiable function such that `f(x) f'(x) lt 0` for all real x, it follows that

A

`f(x)` is an increasing function

B

` f(x)` is a decreasing function

C

` |f(x)|` is an increasing function

D

` |f(x)|` is a decreasing function

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-I) ( Objective Problems ) ( FINDING INTERVALS OF MONOTONOCITY )|2 Videos
  • MONOTONOCITY

    MOTION|Exercise Exercise - 2 (Level-I) ( Objective Problems ) ( FINDING VALUE OF VARIABLE GIVEN MONOTONIC BEHAVIOUR)|3 Videos
  • MONOTONOCITY

    MOTION|Exercise Exercise - 1 ( Objective Problems ) (SECTION-G : BASED ON LMVT)|6 Videos
  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos
  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

Let f(x) and g(x) be differentiable functions such that f'(x)g(x)!=f(x)g'(x) for any real x. Show that between any two real solution of f(x)=0, there is at least one real solution of g(x)=0.

Let f be a real valued function such that f(x)+3xf(1/x)=2(x+1) for all real x > 0. The value of f(5) is

Suppose f is a differentiable real function such that f(x)+f^(prime)(x)lt=1 for all x , and f(0)=0, then the largest possible value of f(1) is (1) e^(-2) (2) e^(-1) (3) 1-e^(-1) (4) 1-e^(-2)

Let f be a real-valued function such that f(x)+2f((2002)/(x))=3x. Then find f(x)

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals