हिंदी

Choose the correct alternative: The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

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

विकल्प

  • increasing for all x ∈ R, x ≠ 1 

  • decreasing

  • neither increasing nor decreasing

  • decreasing for all x ∈ R, x ≠ 1

MCQ

उत्तर

increasing for all x ∈ R, x ≠ 1 

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.4: Applications of Derivatives - Q.1

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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


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) = sin x is

  1. strictly increasing in `(0, pi/2)`
  2. strictly decreasing in `(pi/2, pi)`
  3. neither increasing nor decreasing in (0, π)

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


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.


Prove that the function f given by f(x) = log sin x is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi)`


Let f be a function defined on [a, b] such that f '(x) > 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b).


Show that the function f(x) = 4x3 - 18x2 + 27x - 7 is always increasing on R.


Show that f(x) = \[\frac{1}{1 + x^2}\] is neither increasing nor decreasing on R ?


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) = x4 − 4x3 + 4x2 + 15 ?


Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?


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


Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?


Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?


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


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) ?


Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?


Prove that the function f(x) = cos x is:
(i) strictly decreasing in (0, π)
(ii) strictly increasing in (π, 2π)
(iii) neither increasing nor decreasing in (0, 2π).


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


Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?


If g (x) is a decreasing function on R and f(x) = tan−1 [g (x)]. State whether f(x) is increasing or decreasing 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(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval


The function f(x) = x2 e−x is monotonic increasing when


In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is


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


Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when


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


The radius r of a right circular cylinder is increasing uniformly at the rate of 0·3 cm/s and its height h is decreasing at the rate of 0·4 cm/s. When r = 3·5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. \[\left[ \text{ Use } \pi = \frac{22}{7} \right]\]


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.


Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q 


Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing. 


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


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

f(x) = 3 + 3x – 3x2 + x3


Choose the correct option from the given alternatives :

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


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


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  ______


Find the values of x such that f(x) = 2x3 – 15x2 – 144x – 7 is decreasing function


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


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 ______.


Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` 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") = "x"/"logx"` increases on the interval


Let h(x) = f(x) - [f(x)]2 + [f(x)]3 for every real number x. Then ____________.


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 'a' be a real number such that the function f(x) = ax2 + 6x – 15, x ∈ R is increasing in `(-∞, 3/4)` and decreasing in `(3/4, ∞)`. Then the function g(x) = ax2 – 6x + 15, x∈R has a ______.


If f(x) = x3 + 4x2 + λx + 1(λ ∈ R) is a monotonically decreasing function of x in the largest possible interval `(–2, (–2)/3)` then ______.


The function f(x) = tan–1(sin x + cos x) is an increasing function in ______.


If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.


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×