हिंदी

State whether the following statement is true or false. If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b). - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following statement is true or false.

If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

This statement is False.

Explanation:

If f"(x) > 0 for all x ∈ (a, b), then f(x) is decreasing function in the interval (a, b).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2021-2022 (March) Set 1

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Prove that  y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`


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


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) = 6 − 9x − x2  ?


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 \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?


Show that f(x) = log sin x is increasing on (0, π/2) and decreasing on (π/2, π) ?


The interval of increase of the function f(x) = x − ex + tan (2π/7) is


Let f(x) = x3 − 6x2 + 15x + 3. Then,


Let ϕ(x) = f(x) + f(2a − x) and f"(x) > 0 for all x ∈ [0, a]. Then, ϕ (x)


If the function f(x) = x3 − 9kx2 + 27x + 30 is increasing on R, then


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


If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 ,  Interpret your result. 


Prove that the function f : N → N, defined by f(x) = x2 + x + 1 is one-one but not onto. Find the inverse of f: N → S, where S is range of f.


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


Test whether the following function is increasing or decreasing.

f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0


Choose the correct alternative.

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


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


The total cost function for production of articles is given as C = 100 + 600x – 3x2, then the values of x for which the total cost is decreasing is  ______


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


A man of height 1.9 m walks directly away from a lamp of height 4.75m on a level road at 6m/s. The rate at which the length of his shadow is increasing is


The function f(x) = x3 - 3x is ______.


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 ______


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


The function f(x) = tanx – x ______.


In case of decreasing functions, slope of tangent and hence derivative is ____________.


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


The function f: N → N, where

f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is


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)

The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×