Advertisements
Advertisements
प्रश्न
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
Advertisements
उत्तर
\[f\left( x \right) = \sin x - bx + c\]
\[f'\left( x \right) = \cos x - b\]
\[\text { Given }:f\left( x \right) \text { is decreasing on R }.\]
\[f'\left( x \right) < 0, \forall x \in R\]
\[ \Rightarrow \cos x - b < 0, \forall x \in R\]
\[\Rightarrow\cos x - b < 0, \forall x \in R \]
\[ \Rightarrow \cos x < b, \forall x \in R\]
\[ \Rightarrow b \geqslant 1 \left[ \because - 1 \leqslant \cos x \leqslant 1 \right]\]
APPEARS IN
संबंधित प्रश्न
Find the intervals in which the following functions are strictly increasing or decreasing:
10 − 6x − 2x2
Prove that the function f given by f(x) = x2 − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).
The interval in which y = x2 e–x is increasing is ______.
Show that f(x) = \[\frac{1}{x}\] is a decreasing function 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) = −2x3 − 9x2 − 12x + 1 ?
Show that f(x) = cos2 x is a decreasing function on (0, π/2) ?
Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?
Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x \[\leq 2\pi\] ?
Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?
Function f(x) = cos x − 2 λ x is monotonic decreasing when
Function f(x) = x3 − 27x + 5 is monotonically increasing when ______.
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
Find `dy/dx,if e^x+e^y=e^(x-y)`
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.
Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing.
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 following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Show that f(x) = x – cos x is increasing for all x.
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
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 ______
A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall 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 ______
The function f(x) = sin x + 2x is ______
The interval on which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
Which of the following functions is decreasing on `(0, pi/2)`?
The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.
In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.
If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.
If f(x) = x + cosx – a then ______.
Let f : R `rightarrow` R be a positive increasing function with `lim_(x rightarrow ∞) (f(3x))/(f(x))` = 1 then `lim_(x rightarrow ∞) (f(2x))/(f(x))` = ______.
If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.
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 ______.
