Advertisements
Advertisements
प्रश्न
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
Advertisements
उत्तर
\[f\left( x \right) = \frac{- x}{2} + \sin x\]
\[f'\left( x \right) = \frac{- 1}{2} + \cos x\]
\[\text { Here, }\]
\[ \frac{- \pi}{3} < x < \frac{\pi}{3}\]
\[ \Rightarrow \cos x > \frac{1}{2}\]
\[ \Rightarrow \frac{- 1}{2} + \cos x > 0\]
\[ \Rightarrow f'\left( x \right) > 0, \forall x \in \left( \frac{- \pi}{3}, \frac{\pi}{3} \right)\]
\[\text {So,f }\left( x \right) \text { is increasing on }\left( \frac{- \pi}{3}, \frac{\pi}{3} \right).\]
APPEARS IN
संबंधित प्रश्न
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
Find the intervals in which the following functions are strictly increasing or decreasing:
x2 + 2x − 5
Prove that the function f(x) = loge x is increasing on (0, ∞) ?
Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?
Find the interval in which the following function are increasing or decreasing f(x) = 6 + 12x + 3x2 − 2x3 ?
Find the interval in which the following function are increasing or decreasing f(x) = −2x3 − 9x2 − 12x + 1 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 24x + 7 ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 + 9x + 15 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \left\{ x(x - 2) \right\}^2\] ?
Show that f(x) = tan−1 x − x is a decreasing function on R ?
Show that the function f given by f(x) = 10x is increasing for all x ?
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
State whether f(x) = tan x − x is increasing or decreasing its domain ?
Every invertible function is
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
If the function f(x) = cos |x| − 2ax + b increases along the entire number scale, then
Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R.
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.
Choose the correct option from the given alternatives :
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly decreasing in ______.
State whether the following statement is True or False:
The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
The price P for the demand D is given as P = 183 + 120D − 3D2, then the value of D for which price is increasing, is ______.
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
The function f(x) = x3 - 3x is ______.
The values of k for which the function f(x) = kx3 – 6x2 + 12x + 11 may be increasing on R are ______.
The function f(x) = x2 – 2x is increasing in the interval ____________.
The function f (x) = x2, for all real x, is ____________.
Let h(x) = f(x) - [f(x)]2 + [f(x)]3 for every real number x. Then ____________.
The function f: N → N, where
f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is
Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.
If f(x) = x + cosx – a then ______.
A function f is said to be increasing at a point c if ______.
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.
