English

Let f(x) = x3 − 62 + 9𝑥 + 18, then f(x) is strictly decreasing in ______ - Mathematics and Statistics

Advertisements
Advertisements

Question

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

Options

  • (−∞, 1)

  • (3, ∞)

  • (−∞, 1) ∪ (3, ∞)

  • (1, 3)

MCQ
Fill in the Blanks

Solution

(1, 3)

shaalaa.com
  Is there an error in this question or solution?
Chapter 2.2: Applications of Derivatives - MCQ

RELATED QUESTIONS

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


Find the intervals in which the following functions are strictly increasing or decreasing:

x2 + 2x − 5


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


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


Water is dripping out from a conical funnel of semi-verticle angle `pi/4` at the uniform rate of `2 cm^2/sec`in the surface, through a tiny hole at the vertex of the bottom. When the slant height of the water level is 4 cm, find the rate of decrease of the slant height of the water.


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


Without using the derivative, show that the function f (x) = | x | is.
(a) strictly increasing in (0, ∞)
(b) strictly decreasing in (−∞, 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) = x3 − 12x2 + 36x + 17 ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{10} x^4 - \frac{4}{5} x^3 - 3 x^2 + \frac{36}{5}x + 11\] ?


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


Show that f(x) = x − sin x is increasing for all x ∈ R ?


Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?


Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ? 


Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4) ?


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


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


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


Show that f(x) = x + cos x − a is an increasing function on R for all values of a ?


Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?


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


Let f(x) = x3 − 6x2 + 15x + 3. Then,


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


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


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

 


If the function f(x) = x2 − kx + 5 is increasing on [2, 4], then


The function f(x) = x9 + 3x7 + 64 is increasing on


If x = cos2 θ and y = cot θ then find `dy/dx  at  θ=pi/4` 


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


For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.


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.


The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.


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


Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.


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 increasing function.

f(x) = x2 + 2x - 5 


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

f(x) = 2x3 – 15x2 – 84x – 7 


Choose the correct alternative.

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


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


Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing


The slope of tangent at any point (a, b) is also called as ______.


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


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


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 ______


For which interval the given function f(x) = 2x3 – 9x2 + 12x + 7 is increasing?


The values of k for which the function f(x) = kx3 – 6x2 + 12x + 11 may be increasing on R are ______.


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


Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.


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


Show that f(x) = tan–1(sinx + cosx) is an increasing function in `(0, pi/4)`


The function f(x) = 4 sin3x – 6 sin2x + 12 sinx + 100 is strictly ______.


The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.


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


Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.


If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:


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


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


The function f(x) = x3 + 6x2 + (9 + 2k)x + 1 is strictly increasing for all x, if ____________.


The function f: N → N, where

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


Which of the following graph represent the strictly increasing function.


Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.


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


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 ______.


Let f(x) be a function such that; f'(x) = log1/3(log3(sinx + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is ______.


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


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


Find the interval in which the function f(x) = x2e–x is strictly increasing or decreasing.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×