Advertisements
Advertisements
प्रश्न
The function f(x) = tanx – x ______.
विकल्प
Always increases
Always decreases
Never increases
Sometimes increases and sometimes decreases
Advertisements
उत्तर
The function f(x) = tanx – x always increases.
Explanation:
Here, f(x) = tan x – x
So, f'(x) = sec2x – 1
f'(x) > 0 ∀ x ∈ R
So f(x) is always increasing.
APPEARS IN
संबंधित प्रश्न
Prove that the function f given by f(x) = log cos x is strictly decreasing on `(0, pi/2)` and strictly increasing on `((3pi)/2, 2pi).`
Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R ?
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) = x2 + 2x − 5 ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 12x2 + 36x + 17 ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x3 + 4x2 + 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 ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Show that f(x) = e2x is increasing on R.
Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
State whether f(x) = tan x − x is increasing or decreasing its domain ?
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
Every invertible function is
Function f(x) = loga x is increasing on R, if
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
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.
Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.
Prove that y = `(4sinθ)/(2 + cosθ) - θ` is an increasing function if `θ ∈[0, pi/2]`
Test whether the following function is increasing or decreasing.
f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 – 15x2 – 84x – 7
Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.
Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is
- Strictly increasing
- strictly decreasing
The area of the square increases at the rate of 0.5 cm2/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.
For every value of x, the function f(x) = `1/7^x` is ______
The function `1/(1 + x^2)` is increasing in the interval ______
Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R
The function `"f"("x") = "log" (1 + "x") - (2"x")/(2 + "x")` is increasing on ____________.
The function `"f"("x") = "x"/"logx"` increases on the interval
Let x0 be a point in the domain of definition of a real valued function `f` and there exists an open interval I = (x0 – h, ro + h) containing x0. Then which of the following statement is/ are true for the above statement.
The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is
The function f(x) = sin4x + cos4x is an increasing function if ______.
Let \[f\] be continuous on \[[a,b]\] and differentiable on \[(a,b)\]. If \[f'(x)\leq0\] for every \[x\in(a,b)\], what follows?
After the domain has been divided into intervals, which quantity must be determined in each interval?
Which form shows that \[f'(x)=3x^2-6x+4\] is positive for every \[x\in\mathbf{R}\]?
