English

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

Advertisements
Advertisements

Question

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

Fill in the Blanks

Solution

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

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.4: Applications of Derivatives - Q.2

RELATED QUESTIONS

Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.


Show that the function `f(x) = x^3 - 3x^2 + 6x - 100` is increasing on R


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

10 − 6x − 2x2


Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 0] ?


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


Find the interval in which the following function are increasing or decreasing f(x) = (x − 1) (x − 2)?


Find the interval in which the following function are increasing or decreasing  f(x) = x4 − 4x3 + 4x2 + 15 ?


Find the interval in which the following function are increasing or decreasing  f(x) =  \[5 x^\frac{3}{2} - 3 x^\frac{5}{2}\]  x > 0 ?


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) = sin x − cos x is an increasing function on (−π/4, π/4) ?


Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?


Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?


Prove that the function f given by f(x) = x − [x] is increasing in (0, 1) ?


Prove that the function f given by f(x) = log cos x is strictly increasing on (−π/2, 0) and strictly decreasing on (0, π/2) ?


Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?


Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?


Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?


State whether f(x) = tan x − x is increasing or decreasing its domain ?


Function f(x) = ax is increasing on R, if


If the function f(x) = x2 − kx + 5 is increasing on [2, 4], then


The function f(x) = x9 + 3x7 + 64 is increasing on


The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.


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).


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


For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.


The total cost of manufacturing x articles is C = 47x + 300x2 − x4.  Find x, for which average cost is increasing.


Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x2 – x3, x ∈ R.


Find the values of x for which the following functions are strictly decreasing:

f(x) = 2x3 – 3x2 – 12x + 6


show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.


Show that f(x) = x – cos x is increasing for all x.


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

f(x) = x4 − 2x3 + 1


State whether the following statement is True or False:

The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.


Find the values of x for which the function f(x) = x3 – 6x2 – 36x + 7 is strictly increasing


By completing the following activity, find the values of x such that f(x) = 2x3 – 15x2 – 84x – 7 is decreasing function.

Solution: f(x) = 2x3 – 15x2 – 84x – 7

∴ f'(x) = `square`

∴ f'(x) = 6`(square) (square)`

Since f(x) is decreasing function.

∴ f'(x) < 0

Case 1: `(square)` > 0 and (x + 2) < 0

∴ x ∈ `square`

Case 2: `(square)` < 0 and (x + 2) > 0

∴ x ∈ `square`

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


A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is


The area of the square increases at the rate of 0.5 cm2/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.


The function f(x) = sin x + 2x is ______ 


For which interval the given function f(x) = 2x3 – 9x2 + 12x + 7 is increasing?


In which interval is the given function, f(x) = 2x3 - 21x2 + 72x + 19 monotonically decreasing?


The function `1/(1 + x^2)` is increasing in the interval ______ 


If f(x) = x3 – 15x2 + 84x – 17, then ______.


Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R


The function f(x) = tanx – x ______.


The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.


The function f(x) = mx + c where m, c are constants, is a strict decreasing function for all `"x" in "R"` , if ____________.


The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.


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


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


The function f(x) = tan-1 (sin x + cos x) is an increasing function in:


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`


If f(x) = x + cosx – a then ______.


Let f(x) = `x/sqrt(a^2 + x^2) - (d - x)/sqrt(b^2 + (d - x)^2), x ∈ R` where a, b and d are non-zero real constants. Then ______.


Read the following passage:

The use of electric vehicles will curb air pollution in the long run.

The use of electric vehicles is increasing every year and the estimated electric vehicles in use at any time t is given by the function V:

V(t) = `1/5 t^3 - 5/2 t^2 + 25t - 2`

where t represents the time and t = 1, 2, 3, ...... corresponds to years 2001, 2002, 2003, ...... respectively.

Based on the above information, answer the following questions:

  1. Can the above function be used to estimate number of vehicles in the year 2000? Justify. (2)
  2. Prove that the function V(t) is an increasing function. (2)

Find the interval/s in which the function f : R `rightarrow` R defined by f(x) = xex, is increasing.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×