Advertisements
Advertisements
प्रश्न
Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?
Advertisements
उत्तर
\[f\left( x \right) = \sin x - ax + 4\]
\[f'\left( x \right) = \cos x - a\]
\[\text { Given }:f(x) \text { is increasing on R }.\]
\[ \Rightarrow f'\left( x \right) > 0\]
\[ \Rightarrow \cos x - a > 0\]
\[ \Rightarrow \cos x > a \]
\[\text { We know,}\]
\[\cos x \geq - 1, \forall x \in R \]
\[ \Rightarrow a < - 1\]
\[ \Rightarrow a \in \left( - \infty , - 1 \right)\]
APPEARS IN
संबंधित प्रश्न
Find the intervals in which the following functions are strictly increasing or decreasing:
−2x3 − 9x2 − 12x + 1
Prove that y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`
Find the least value of a such that the function f given by f (x) = x2 + ax + 1 is strictly increasing on [1, 2].
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
Find the interval in which the following function are increasing or decreasing f(x) = 10 − 6x − 2x2 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 12x2 + 18x + 15 ?
Determine the values of x for which the function f(x) = x2 − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x2 − 6x + 9 where the normal is parallel to the line y = x + 5 ?
Show that f(x) = e2x is increasing on R.
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
Show that f(x) = x + cos x − a is an increasing function on R for all values of a ?
Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
The function f(x) = xx decreases on the interval
If the function f(x) = 2 tan x + (2a + 1) loge | sec x | + (a − 2) x is increasing on R, then
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) = x3 − 27x + 5 is monotonically increasing when ______.
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
If the function f(x) = x3 − 9kx2 + 27x + 30 is increasing on R, then
Find `dy/dx,if e^x+e^y=e^(x-y)`
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
Show that f(x) = x – cos x is increasing for all x.
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 increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.
If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______
State whether the following statement is True or False:
The function f(x) = `3/x` + 10, x ≠ 0 is decreasing
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.
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 ______
Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.
Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
The function f(x) = x3 + 6x2 + (9 + 2k)x + 1 is strictly increasing for all x, if ____________.
`"f"("x") = (("e"^(2"x") - 1)/("e"^(2"x") + 1))` is ____________.
The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is
The function f(x) = tan–1(sin x + cos x) is an increasing function in ______.
A function f is said to be increasing at a point c if ______.
