मराठी
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

Advertisements
Advertisements

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
Advertisements

उत्तर

increasing for all x ∈ R, x ≠ 1 

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

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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


Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is

  1. Strictly increasing
  2. Strictly decreasing

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


Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \left\{ x(x - 2) \right\}^2\] ?


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


Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?


Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?


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).


Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?


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


Let f defined on [0, 1] be twice differentiable such that | f (x) | ≤ 1 for all x ∈ [0, 1]. If f(0) = f(1), then show that | f'(x) | < 1 for all x ∈ [ 0, 1] ?


The function f(x) = xx decreases on the interval


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


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.


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

f(x) = 2x3 – 3x2 – 12x + 6


Find the values of x for which the function f(x) = x3 – 12x2 – 144x + 13 (a) increasing (b) decreasing


State whether the following statement is True or False:

The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.


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


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


A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is


In which interval is the given function, f(x) = 2x3 - 21x2 + 72x + 19 monotonically decreasing?


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


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


The function `"f"("x") = "x"/"logx"` increases on the interval


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 ______.


Let \[f\] be continuous on \[[a,b]\] and differentiable on \[(a,b)\]. If \[f'(x)\leq0\] for every \[x\in(a,b)\], what follows?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×