Advertisements
Advertisements
Question
The values of a for which the function f(x) = sinx – ax + b increases on R are ______.
Advertisements
Solution
The values of a for which the function f(x) = sinx – ax + b increases on R are `(-oo, -1)`.
Explanation:
We have f(x) = sin x – ax + b
⇒ f'(x) = cos x – a
For increasing the function f'(x) > 0
∴ cos x – a > 0
Since `cos x ∈ [-1, 1]`
∴ a < –1
⇒ `"a" ∈ (-oo, -1)`
Hence, the value of a is `"a" ∈ (-oo, -1)`.
APPEARS IN
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 function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
Prove that the logarithmic function is strictly increasing on (0, ∞).
Which of the following functions are strictly decreasing on `(0, pi/2)`?
- cos x
- cos 2x
- cos 3x
- tan x
Find the intervals in which the function f given by `f(x) = (4sin x - 2x - x cos x)/(2 + cos x)` is (i) increasing (ii) decreasing.
Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 0] ?
Show that f(x) = e2x is increasing on R.
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all 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 ?
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) ?
Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?
Let \[f\left( x \right) = \tan^{- 1} \left( g\left( x \right) \right),\],where g (x) is monotonically increasing for 0 < x < \[\frac{\pi}{2} .\] Then, f(x) is
Function f(x) = cos x − 2 λ x is monotonic decreasing when
Function f(x) = | x | − | x − 1 | is monotonically increasing 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
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
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.
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Solve the following : Find the intervals on which the function y = xx, (x > 0) is increasing and decreasing.
Find the value of x such that f(x) is decreasing function.
f(x) = x4 − 2x3 + 1
Choose the correct alternative.
The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is
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 + 36x + 1 is increasing function
Find the values of x such that f(x) = 2x3 – 15x2 – 144x – 7 is decreasing function
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
If f(x) = `x^(3/2) (3x - 10)`, x ≥ 0, then f(x) is increasing in ______.
Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.
The function f (x) = 2 – 3 x is ____________.
The function f (x) = x2, for all real x, is ____________.
In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.
The function `"f"("x") = "x"/"logx"` increases on the interval
The function f: N → N, where
f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is
Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.
The function f(x) = x3 + 3x is increasing in interval ______.
For \[f(x)=x^3-3x^2+4x\], what is \[f'(x)\]?
