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

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

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प्रश्न

Choose the correct alternative:

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

पर्याय

  • increasing for all x ∈ R, x ≠ 1 

  • decreasing

  • neither increasing nor decreasing

  • decreasing for all x ∈ R, x ≠ 1

MCQ
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उत्तर

increasing for all x ∈ R, x ≠ 1 

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.4: Applications of Derivatives - Q.1

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Find the intervals in which the function f(x) = 3x4 − 4x3 − 12x2 + 5 is

(a) strictly increasing

(b) strictly decreasing


Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing.


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


Find the least value of a such that the function f given by f (x) = x2 + ax + 1 is strictly increasing on [1, 2].


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


Find the intervals in which the function `f(x) = x^4/4 - x^3 - 5x^2 + 24x + 12`  is (a) strictly increasing, (b) strictly decreasing


Prove that the function f(x) = loge x is increasing on (0, ∞) ?


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) = x4 − 4x3 + 4x2 + 15 ?


Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 + 9x + 15 ?


Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?


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


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


Find the value(s) of a for which f(x) = x3 − ax is an increasing function on R ?


Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?


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

 


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


Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.


Test whether the following function f(x) = 2 – 3x + 3x2 – x3, x ∈ R is increasing or decreasing


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

  1. Strictly increasing
  2. strictly decreasing

State whether the following statement is True or False: 

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


Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`


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


y = x(x – 3)2 decreases for the values of x given by : ______.


Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.


The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.


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


The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.


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