English

The function f(x) = x-1x, x ∈ R, x ≠ 0 is increasing - Mathematics and Statistics

Advertisements
Advertisements

Question

The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing

Options

  • True

  • False

MCQ
True or False

Solution

This Statement is True.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.4: Applications of Derivatives - Q.3

APPEARS IN

RELATED QUESTIONS

Find the value of c in Rolle's theorem for the function `f(x) = x^3 - 3x " in " (-sqrt3, 0)`


Find the intervals in which the following functions are strictly increasing or decreasing:

6 − 9x − x2


Show that y = `log(1+x) - (2x)/(2+x), x> -  1`, is an increasing function of x throughout its domain.


Prove that the logarithmic function is strictly increasing on (0, ∞).


Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.


Find the intervals in which the function f given by `f(x) = (4sin x - 2x - x cos x)/(2 + cos x)` is (i) increasing (ii) decreasing.


Find the interval in which the following function are increasing or decreasing f(x) = 6 + 12x + 3x2 − 2x3 ?


Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 + 9x + 15 ?


Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?


Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?


Find the value(s) of a for which f(x) = x3 − ax is an increasing function on R ?


Write the set of values of a for which f(x) = cos x + a2 x + b is strictly increasing on R ?


The function \[f\left( x \right) = \frac{x}{1 + \left| x \right|}\] is 

 


Find `dy/dx,if e^x+e^y=e^(x-y)`


 Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R. 


The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.


Test whether the following functions are increasing or decreasing : f(x) = `(1)/x`, x ∈ R , x ≠ 0.


Solve the following : Find the intervals on which the function y = xx, (x > 0) is increasing and decreasing.


Find the value of x, such that f(x) is increasing function.

f(x) = x2 + 2x - 5 


Test whether the function f(x) = x3 + 6x2 + 12x − 5 is increasing or decreasing for all x ∈ R


Test whether the following function f(x) = 2 – 3x + 3x2 – x3, x ∈ R is increasing or decreasing


If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______


The sides of a square are increasing at the rate of 0.2 cm/sec. When the side is 25cm long, its area is increasing at the rate of ______


If f(x) = `x^(3/2) (3x - 10)`, x ≥ 0, then f(x) is increasing in ______.


Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.


The function f(x) = tanx – x ______.


The function f(x) = x2 – 2x is increasing in the interval ____________.


In `(0, pi/2),`  the function f (x) = `"x"/"sin x"` is ____________.


2x3 - 6x + 5 is an increasing function, if ____________.


The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.


`"f"("x") = (("e"^(2"x") - 1)/("e"^(2"x") + 1))` is ____________.


The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is


Find the value of x for which the function f(x)= 2x3 – 9x2 + 12x + 2 is decreasing.

Given f(x) = 2x3 – 9x2 + 12x + 2

∴ f'(x) = `squarex^2 - square + square`

∴ f'(x) = `6(x - 1)(square)`

Now f'(x) < 0

∴ 6(x – 1)(x – 2) < 0

Since ab < 0 ⇔a < 0 and b < 0 or a > 0 and b < 0

Case 1: (x – 1) < 0 and (x – 2) < 0

∴ x < `square` and x > `square`

Which is contradiction

Case 2: x – 1 and x – 2 < 0

∴ x > `square` and x < `square`

1 < `square` < 2

f(x) is decreasing if and only if x ∈ `square`


The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.


If f(x) = x + cosx – a then ______.


Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×