Advertisements
Advertisements
प्रश्न
y = x(x – 3)2 decreases for the values of x given by : ______.
विकल्प
1 < x < 3
x < 0
x > 0
`0 < x < 3/2`
Advertisements
उत्तर
y = x(x – 3)2 decreases for the values of x given by : 1 < x < 3.
Explanation:
Here y = x(x – 3)2
`"dy"/"dx" = x * 2(x - 3) + (x - 3)^2 * 1`
⇒ `"dy"/"dx" = 2x(x - 3) + (x - 3)^2`
For increasing and decreasing `"dy"/"dx"` = 0
∴ 2x(x – 3) + (x – 3)2 = 0
⇒ (x – 3)(2x + x – 3) = 0
⇒ (x – 3)(3x – 3) = 0
⇒ 3(x – 3)(x – 1) = 0
∴ x = 1, 3
∴ Possible intervals are `(– oo, 1), (1, 3), (3, oo)`
`"dy"/"dx"` = (x – 3)(x – 1)
For `(– oo, 1)` = (–) (–) = (+) increasing
For (1, 3) = (–) (+) = (–) decreasing
For `(3, oo)` = (+) (+) = (+) increasing
So the function decreases in (1, 3) or 1 < x < 3
APPEARS IN
संबंधित प्रश्न
Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing.
Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.
Find the intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
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).
Find the intervals in which the function `f(x) = x^4/4 - x^3 - 5x^2 + 24x + 12` is (a) strictly increasing, (b) strictly decreasing
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \left\{ x(x - 2) \right\}^2\] ?
Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
Show that f(x) = sin x is an increasing function on (−π/2, π/2) ?
Show that the function f(x) = cot \[-\] l(sinx + cosx) is decreasing on \[\left( 0, \frac{\pi}{4} \right)\] and increasing on \[\left( 0, \frac{\pi}{4} \right)\] ?
Prove that the function f(x) = cos x is:
(i) strictly decreasing in (0, π)
(ii) strictly increasing in (π, 2π)
(iii) neither increasing nor decreasing in (0, 2π).
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
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) = sinx(1 + cosx), 0 < x < \[\frac{\pi}{2}\] ?
What are the values of 'a' for which f(x) = ax is decreasing on R ?
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
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
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`
Find `dy/dx,if e^x+e^y=e^(x-y)`
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.
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 function f(x) = x3 – 12x2 – 144x + 13 (a) increasing (b) decreasing
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.
The function f(x) = 9 - x5 - x7 is decreasing for
The function f(x) = x3 - 3x is ______.
The function f(x) = 4 sin3x – 6 sin2x + 12 sinx + 100 is strictly ______.
The function f (x) = 2 – 3 x is ____________.
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
The function f(x) = tan-1 (sin x + cos x) is an increasing function in:
`"f"("x") = (("e"^(2"x") - 1)/("e"^(2"x") + 1))` is ____________.
The function `"f"("x") = "x"/"logx"` increases on the interval
Which of the following graph represent the strictly increasing function.
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) = x3 + 3x is increasing in interval ______.
Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.
