मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

A function f is said to be increasing at a point c if ______. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

A function f is said to be increasing at a point c if ______.

पर्याय

  • f'(c) = 0

  • f'(c) > 0

  • f'(c) < 0

  • f'(c) = 1

MCQ
रिकाम्या जागा भरा

उत्तर

A function f is said to be increasing at a point c if f'(c) > 0.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2022-2023 (March) Official

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.


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 ?


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


Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 


Show that the function given by f(x) = 3x + 17 is strictly increasing on R.


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


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


On which of the following intervals is the function f given byf(x) = x100 + sin x –1 strictly decreasing?


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


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


Without using the derivative, show that the function f (x) = | x | is.
(a) strictly increasing in (0, ∞)
(b) strictly decreasing in (−∞, 0) .


Without using the derivative show that the function f (x) = 7x − 3 is strictly increasing function on R ?


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) = x3 − 6x2 − 36x + 2 ?


Find the interval in which the following function are increasing or decreasing f(x) = 2x3 + 9x2 + 12x + 20  ?


Find the interval in which the following function are increasing or decreasing  f(x) = 2x3 − 24x + 107  ?


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 ?


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


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) = tan−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?


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) = x|x|, x \[\in\] R ?


Find the interval in which f(x) is increasing or decreasing f(x) = sinx(1 + cosx), 0 < x < \[\frac{\pi}{2}\] ?


What are the values of 'a' for which f(x) = ax is increasing on R ?


Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?


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


Let f(x) = x3 + ax2 + bx + 5 sin2x be an increasing function on the set R. Then, a and b satisfy.


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


Function f(x) = x3 − 27x + 5 is monotonically increasing when


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

 


The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if

 


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


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).


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


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

f(x) = x4 − 2x3 + 1


Show that the function f(x) = x3 + 10x + 7 for x ∈ R is strictly increasing


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

(a) Strictly increasing
(b) strictly decreasing


Choose the correct alternative:

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


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


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  ______


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


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 ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall 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 ______


Given P(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P'(x) = 0. If P(-1) < P(1), then in the interval [-1, 1] ______


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


The values of a for which the function f(x) = sinx – ax + b increases on R are ______.


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


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


Which of the following graph represent the strictly increasing function.


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)

Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.


The function f(x) = sin4x + cos4x is an increasing function if ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×