Advertisements
Advertisements
प्रश्न
Which of the following functions is decreasing on `(0, pi/2)`?
पर्याय
sin2x
tanx
cosx
cos 3x
उत्तर
cosx
Explanation:
Here, Let f x) = cos x
So, f'(x) = – sin x
f'(x) < 0 in `(0, pi/2)`
So f(x) = cos x is decreasing in `(0, pi/2)`
APPEARS IN
संबंधित प्रश्न
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
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:
x2 + 2x − 5
Prove that the function f given by f(x) = x2 − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).
Show that f(x) = e2x is increasing on R.
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Find the value(s) of a for which f(x) = x3 − ax is an increasing function on R ?
Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x \[\leq 2\pi\] ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?
If the function f(x) = 2 tan x + (2a + 1) loge | sec x | + (a − 2) x is increasing on R, then
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).
The total cost of manufacturing x articles is C = 47x + 300x2 − x4. Find x, for which average cost is increasing.
The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Choose the correct option from the given alternatives :
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly decreasing in ______.
Solve the following : Find the intervals on which the function y = xx, (x > 0) is increasing and decreasing.
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.
Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function
Choose the correct alternative:
The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
Show that f(x) = tan–1(sinx + cosx) is an increasing function in `(0, pi/4)`
The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
Let 'a' be a real number such that the function f(x) = ax2 + 6x – 15, x ∈ R is increasing in `(-∞, 3/4)` and decreasing in `(3/4, ∞)`. Then the function g(x) = ax2 – 6x + 15, x∈R has a ______.
If f(x) = x + cosx – a then ______.
The function f(x) = tan–1(sin x + cos x) is an increasing function in ______.
If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.