Advertisements
Advertisements
प्रश्न
Let the f : R → R be defined by f (x) = 2x + cosx, then f : ______.
विकल्प
has a minimum at x = π
has a maximum, at x = 0
is a decreasing function
is an increasing function
Advertisements
उत्तर
Let the f : R → R be defined by f (x) = 2x + cosx, then f : is an increasing function.
Explanation:
Given that f(x) = 2x + cos x
f'(x) = 2 – sin x
Since f'(x) > 0 ∀ x
So f(x) is an increasing function.
APPEARS IN
संबंधित प्रश्न
Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing.
Show that the function `f(x) = x^3 - 3x^2 + 6x - 100` is increasing on R
Show that the function given by f(x) = sin x is
- strictly increasing in `(0, pi/2)`
- strictly decreasing in `(pi/2, pi)`
- neither increasing nor decreasing in (0, π)
Find the intervals in which the following functions are strictly increasing or decreasing:
x2 + 2x − 5
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 + 12x + 3x2 − 2x3 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?
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 ?
Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?
Show that f(x) = tan−1 x − x is a decreasing function on R ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
If the function f(x) = 2x2 − kx + 5 is increasing on [1, 2], then k lies in the interval
Function f(x) = cos x − 2 λ x is monotonic decreasing when
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
The function \[f\left( x \right) = \frac{x}{1 + \left| x \right|}\] is
If the function f(x) = x2 − kx + 5 is increasing on [2, 4], then
Find the intervals in which function f given by f(x) = 4x3 - 6x2 - 72x + 30 is (a) strictly increasing, (b) strictly decresing .
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.
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
Let f(x) = x3 − 6x2 + 9𝑥 + 18, then f(x) is strictly decreasing in ______
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
Find the values of x such that f(x) = 2x3 – 15x2 – 144x – 7 is decreasing function
If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.
If f(x) = x3 – 15x2 + 84x – 17, then ______.
The function f(x) = 4 sin3x – 6 sin2x + 12 sinx + 100 is strictly ______.
Which of the following functions is decreasing on `(0, pi/2)`?
The function f(x) = tanx – x ______.
The function f (x) = 2 – 3 x is ____________.
Function given by f(x) = sin x is strictly increasing in.
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 ______.
If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
