Advertisements
Advertisements
प्रश्न
If the function f(x) = x2 − kx + 5 is increasing on [2, 4], then
विकल्प
k ∈ (2, ∞)
k ∈ (−∞, 2)
k ∈ (4, ∞)
k ∈ (−∞, 4).
Advertisements
उत्तर
k ∈ (−∞, 4)
\[f\left( x \right) = x^2 - kx + 5\]
\[f'\left( x \right) = 2x - k\]
\[\text { Given: f(x) is increasing on } [2, 4] . \]
\[ \Rightarrow f'\left( x \right) > 0\]
\[ \Rightarrow 2x - k > 0\]
\[ \Rightarrow k < 2x\]
\[\because x \in \left[ 2, 4 \right], \text { maximum value of k is} 4,k< 4.\]
\[ \therefore k \in \left( - \infty , 4 \right)\]
APPEARS IN
संबंधित प्रश्न
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:
−2x3 − 9x2 − 12x + 1
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 f given by f(x) = log sin x is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi)`
Let f be a function defined on [a, b] such that f '(x) > 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b).
Prove that the function f(x) = loge x is increasing on (0, ∞) ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 15x2 + 36x + 1 ?
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?
Write the set of values of k for which f(x) = kx − sin x is increasing on R ?
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
Let f(x) = x3 − 6x2 + 15x + 3. Then,
Function f(x) = | x | − | x − 1 | is monotonically increasing when
Every invertible function is
The function \[f\left( x \right) = \frac{x}{1 + \left| x \right|}\] is
Find the intervals in which the function \[f(x) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] is
(a) strictly increasing
(b) strictly decreasing
The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.
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.
State whether the following statement is True or False:
The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.
The slope of tangent at any point (a, b) is also called as ______.
If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.
The function f (x) = x2, for all real x, is ____________.
2x3 - 6x + 5 is an increasing function, if ____________.
If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, 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 ____________.
`"f"("x") = (("e"^(2"x") - 1)/("e"^(2"x") + 1))` is ____________.
Let h(x) = f(x) - [f(x)]2 + [f(x)]3 for every real number x. Then ____________.
Which of the following graph represent the strictly increasing function.
The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.
Let 'a' be a real number such that the function f(x) = ax2 + 6x – 15, x ∈ R is increasing in `(-∞, 3/4)` and decreasing in `(3/4, ∞)`. Then the function g(x) = ax2 – 6x + 15, x∈R has a ______.
Let f: [0, 2]→R be a twice differentiable function such that f"(x) > 0, for all x ∈( 0, 2). If `phi` (x) = f(x) + f(2 – x), then `phi` is ______.
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 function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
The interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.
