Advertisements
Advertisements
प्रश्न
The function f(x) = x3 + 3x is increasing in interval ______.
विकल्प
(– ∞, 0)
(0, ∞)
R
(0, 1)
Advertisements
उत्तर
The function f(x) = x3 + 3x is increasing in interval R.
Explanation:
f(x) = x3 + 3x
`\implies` f'(x) = 3x2 + 3
= 3(x2 + 1) > 0
So function increases for all real values of x ∈ R.
APPEARS IN
संबंधित प्रश्न
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
Show that the function given by f(x) = 3x + 17 is strictly increasing on R.
Find the intervals in which the following functions are strictly increasing or decreasing:
x2 + 2x − 5
Show that y = `log(1+x) - (2x)/(2+x), x> - 1`, is an increasing function of x throughout its domain.
The interval in which y = x2 e–x is increasing is ______.
Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 0] ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 − 36x + 2 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 9x2 + 12x − 5 ?
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) = tan−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?
Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?
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
If the function f(x) = kx3 − 9x2 + 9x + 3 is monotonically increasing in every interval, then
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
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.
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).
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Choose the correct alternative:
The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is
For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.
Let f(x) = x3 + 9x2 + 33x + 13, then f(x) is ______.
Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
State whether the following statement is true or false.
If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.
