Advertisements
Advertisements
Question
State whether f(x) = tan x − x is increasing or decreasing its domain ?
Advertisements
Solution
APPEARS IN
RELATED QUESTIONS
Show that the function given by f(x) = 3x + 17 is strictly increasing on R.
Find the intervals in which the following functions are strictly increasing or decreasing:
−2x3 − 9x2 − 12x + 1
Prove that the function f given by f(x) = x2 − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).
Find the least value of a such that the function f given by f (x) = x2 + ax + 1 is strictly increasing on [1, 2].
Let I be any interval disjoint from (−1, 1). Prove that the function f given by `f(x) = x + 1/x` is strictly increasing on I.
Prove that the function f(x) = loge x is increasing on (0, ∞) ?
Show that f(x) = \[\frac{1}{1 + x^2}\] is neither increasing nor decreasing on R ?
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 \[f\left( x \right) = \log\left( 2 + x \right) - \frac{2x}{2 + x}, x \in R\] ?
Show that f(x) = e2x is increasing on R.
Show that f(x) = log sin x is increasing on (0, π/2) and decreasing on (π/2, π) ?
Show that f(x) = sin x is an increasing function on (−π/2, π/2) ?
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?
Prove that the function f given by f(x) = log cos x is strictly increasing on (−π/2, 0) and strictly decreasing on (0, π/2) ?
Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?
Write the set of values of k for which f(x) = kx − sin x is increasing on R ?
The function f(x) = xx decreases on the interval
Let f(x) = x3 + ax2 + bx + 5 sin2x be an increasing function on the set R. Then, a and b satisfy.
Let f(x) = x3 − 6x2 + 15x + 3. Then,
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`
Find `dy/dx,if e^x+e^y=e^(x-y)`
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Find the values of x for which the following functions are strictly decreasing : f(x) = x3 – 9x2 + 24x + 12
Solve the following:
Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.
For which interval the given function f(x) = 2x3 – 9x2 + 12x + 7 is increasing?
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
Show that f(x) = tan–1(sinx + cosx) is an increasing function in `(0, pi/4)`
Which of the following functions is decreasing on `(0, pi/2)`?
Let f(x) be a function such that; f'(x) = log1/3(log3(sinx + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is ______.
Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
Let \[f\] be continuous on \[[a,b]\] and differentiable on \[(a,b)\]. If \[f'(x)\leq0\] for every \[x\in(a,b)\], what follows?
In the procedure for finding intervals, which conclusion is correct when \[f'(x)<0\]?
For \[f'(x)=12(x-3)(x+2)\], what is the nature of \[f\] on \[(-2,3)\]?
