हिंदी

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

Advertisements
Advertisements

प्रश्न

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

रिक्त स्थान भरें

उत्तर

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

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.4: Applications of Derivatives - Q.2

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing


The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?


Let I be any interval disjoint from (−1, 1). Prove that the function f given by `f(x) = x + 1/x` is strictly increasing on I.


The interval in which y = x2 e–x is increasing is ______.


Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?


Find the interval in which the following function are increasing or decreasing   f(x) = 2x3 − 12x2 + 18x + 15 ?


Find the interval in which the following function are increasing or decreasing  f(x) = 5x3 − 15x2 − 120x + 3 ?


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) = x3 − 6x2 + 9x + 15 ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = 3 x^4 - 4 x^3 - 12 x^2 + 5\] ?


Determine the values of x for which the function f(x) = x2 − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x2 − 6x + 9 where the normal is parallel to the line y = x + 5 ? 


Show that f(x) = e2x is increasing on R.


Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?


Show that the function f(x) = cot \[-\] l(sinx + cosx) is decreasing on \[\left( 0, \frac{\pi}{4} \right)\] and increasing on \[\left( 0, \frac{\pi}{4} \right)\] ?


Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?


Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ? 


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


Find the intervals in which f(x) = (x + 2) e−x is increasing or decreasing ?


Show that the function f given by f(x) = 10x is increasing for all x ?


Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x \[\leq 2\pi\] ?


Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?


Write the set of values of k for which f(x) = kx − sin x is increasing on R ?


The function f(x) = cot−1 x + x increases in the interval


The function f(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval


Let \[f\left( x \right) = \tan^{- 1} \left( g\left( x \right) \right),\],where g (x) is monotonically increasing for 0 < x < \[\frac{\pi}{2} .\] Then, f(x) is


Every invertible function is


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

 


Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6


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


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


Test whether the following function is increasing or decreasing.

f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0


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

f(x) = 2x3 - 15x2 - 144x - 7 


Choose the correct alternative.

The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is


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) = 2x3 – 6x2 + 6x + 24 is strictly increasing


Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is

(a) Strictly increasing
(b) strictly decreasing


State whether the following statement is True or False: 

The function f(x) = `3/x` + 10, x ≠ 0 is decreasing


Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing


The function f(x) = 9 - x5 - x7 is decreasing for


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


Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R


Let the f : R → R be defined by f (x) = 2x + cosx, then f : ______.


The function f(x) = tanx – x ______.


The function f (x) = 2 – 3 x is ____________.


The function f(x) = tan-1 x is ____________.


Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.


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


The length of the longest interval, in which the function `3  "sin x" - 4  "sin"^3"x"` is increasing, is ____________.


Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.


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


Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.


Function f(x) = x100 + sinx – 1 is increasing for all x ∈ ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×