Advertisements
Advertisements
प्रश्न
Show that function f(x) = tan x is increasing in `(0, π/2)`.
Advertisements
उत्तर
Given, f(x) = tan x
f'(x) = sec2x
But sec2x > 0, ∀x∈ (0, π/2)
Hence f(x) = tan x is strictly increasing in (0, π/2).
APPEARS IN
संबंधित प्रश्न
Find the intervals in which the function f given by `f(x) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.
Find the interval in which the following function are increasing or decreasing f(x) = 5x3 − 15x2 − 120x + 3 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 9x2 + 12x − 5 ?
Find the interval in which the following function are increasing or decreasing f(x) = (x − 1) (x − 2)2 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?
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 the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Show that f(x) = tan−1 x − x is a decreasing function on R ?
Prove that the function f given by f(x) = x − [x] is increasing in (0, 1) ?
Let f defined on [0, 1] be twice differentiable such that | f (x) | ≤ 1 for all x ∈ [0, 1]. If f(0) = f(1), then show that | f'(x) | < 1 for all x ∈ [ 0, 1] ?
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 increasing on R ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
Write the set of values of k for which f(x) = kx − sin x is increasing on R ?
Function f(x) = cos x − 2 λ x is monotonic decreasing when
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
Every invertible function is
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
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).
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.
Find the values of x for which the following functions are strictly decreasing:
f(x) = 2x3 – 3x2 – 12x + 6
Find the values of x for which the function f(x) = x3 – 12x2 – 144x + 13 (a) increasing (b) decreasing
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 increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Find the value of x such that f(x) is decreasing function.
f(x) = x4 − 2x3 + 1
Choose the correct alternative.
The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is
Let f(x) = x3 − 6x2 + 9𝑥 + 18, then f(x) is strictly decreasing in ______
Show that f(x) = x – cos x is increasing for all x.
Test whether the function f(x) = x3 + 6x2 + 12x − 5 is increasing or decreasing for all x ∈ R
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
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
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 ______.
The function f(x) = x3 - 3x is ______.
f(x) = `{{:(0"," x = 0 ), (x - 3"," x > 0):}` The function f(x) is ______
Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.
Which of the following functions is decreasing on `(0, pi/2)`?
The function f (x) = 2 – 3 x is ____________.
The function f(x) = x3 + 6x2 + (9 + 2k)x + 1 is strictly increasing for all x, if ____________.
The function f: N → N, where
f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` 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 function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
Function f(x) = x100 + sinx – 1 is increasing for all x ∈ ______.
Let f : R `rightarrow` R be a positive increasing function with `lim_(x rightarrow ∞) (f(3x))/(f(x))` = 1 then `lim_(x rightarrow ∞) (f(2x))/(f(x))` = ______.
The function f(x) = tan–1(sin x + cos x) is an increasing function in ______.
A function f is said to be increasing at a point c if ______.
