Advertisements
Advertisements
प्रश्न
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
पर्याय
increasing
decreasing
constant
none of these
Advertisements
उत्तर
decreasing
\[\text { Given }: f\left( x \right) = 2\left| x - 1 \right| + 3\left| x - 2 \right|\]
\[\text { If 1 < x < 2, then }\left| x - 1 \right| = x - 1 . \]
\[ \Rightarrow \left| x - 2 \right| = - \left( x - 2 \right)\]
\[\text { Now,}\]
\[f\left( x \right) = 2\left| x - 1 \right| + 3\left| x - 2 \right|\]
\[ = 2 \left( x - 1 \right) + 3 \left( - x + 2 \right)\]
\[ = 2x - 2 - 3x + 6\]
\[ = - x + 4\]
\[f'\left( x \right) = - 1 < 0\]
\[\text { So,}f\left( x \right) \text { is decreasing when 1 < x < 2 } .\]
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:
10 − 6x − 2x2
Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{10} x^4 - \frac{4}{5} x^3 - 3 x^2 + \frac{36}{5}x + 11\] ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x3 + 4x2 + 15 ?
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
Find the value(s) of a for which f(x) = x3 − ax is an increasing function on R ?
What are the values of 'a' for which f(x) = ax is increasing on R ?
Find 'a' for which f(x) = a (x + sin x) + a 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
The function f(x) = x2 e−x is monotonic increasing when
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
Function f(x) = | x | − | x − 1 | is monotonically increasing when
The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
Find MPC ( Marginal propensity to Consume ) and APC ( Average Propensity to Consume ) if the expenditure Ec of a person with income I is given as Ec = ( 0.0003 ) I2 + ( 0.075 ) I when I = 1000.
Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x2 – x3, x ∈ R.
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Find the values of x for which the following func- tions are strictly increasing : f(x) = x3 – 6x2 – 36x + 7
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.
Test whether the following function is increasing or decreasing.
f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
State whether the following statement is True or False:
The function f(x) = `3/x` + 10, x ≠ 0 is decreasing
State whether the following statement is True or False:
If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.
The function f(x) = tanx – x ______.
The function f(x) = tan-1 (sin x + cos x) is an increasing function in:
The length of the longest interval, in which the function `3 "sin x" - 4 "sin"^3"x"` is increasing, is ____________.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
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 ______.
The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
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 ______.
Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.
