Advertisements
Advertisements
प्रश्न
The function f(x) = tanx – x ______.
विकल्प
Always increases
Always decreases
Never increases
Sometimes increases and sometimes decreases
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
The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.
(A) increasing
(B) decreasing
(C) increasing and decreasing
(D) neither increasing nor decreasing
Find the intervals in which the following functions are strictly increasing or decreasing:
−2x3 − 9x2 − 12x + 1
Find the intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
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)`
Find the interval in which the following function are increasing or decreasing f(x) = x8 + 6x2 ?
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Show that f(x) = x + cos x − a is an increasing function on R for all values of a ?
Write the set of values of 'a' for which f(x) = loga x is increasing in its domain ?
If the function f(x) = 2x2 − kx + 5 is increasing on [1, 2], then k lies in the interval
The function \[f\left( x \right) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right)\] is of the following types:
Find `dy/dx,if e^x+e^y=e^(x-y)`
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 – 15x2 – 84x – 7
A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is
A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______
For every value of x, the function f(x) = `1/7^x` is ______
The function f(x) = mx + c where m, c are constants, is a strict decreasing function for all `"x" in "R"` , if ____________.
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
The length of the longest interval, in which the function `3 "sin x" - 4 "sin"^3"x"` is increasing, is ____________.
Which of the following graph represent the strictly increasing function.
The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is
Find the value of x for which the function f(x)= 2x3 – 9x2 + 12x + 2 is decreasing.
Given f(x) = 2x3 – 9x2 + 12x + 2
∴ f'(x) = `squarex^2 - square + square`
∴ f'(x) = `6(x - 1)(square)`
Now f'(x) < 0
∴ 6(x – 1)(x – 2) < 0
Since ab < 0 ⇔a < 0 and b < 0 or a > 0 and b < 0
Case 1: (x – 1) < 0 and (x – 2) < 0
∴ x < `square` and x > `square`
Which is contradiction
Case 2: x – 1 and x – 2 < 0
∴ x > `square` and x < `square`
1 < `square` < 2
f(x) is decreasing if and only if x ∈ `square`
If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.
y = log x satisfies for x > 1, the inequality ______.
Function f(x) = x100 + sinx – 1 is increasing for all x ∈ ______.
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
Find the interval in which the function f(x) = x2e–x is strictly increasing or decreasing.
