Advertisements
Advertisements
Question
Let f(x) = x3 − 6x2 + 9𝑥 + 18, then f(x) is strictly decreasing in ______
Options
(−∞, 1)
(3, ∞)
(−∞, 1) ∪ (3, ∞)
(1, 3)
Advertisements
Solution
(1, 3)
APPEARS IN
RELATED QUESTIONS
Find the intervals in which the function f(x) = 3x4 − 4x3 − 12x2 + 5 is
(a) strictly increasing
(b) strictly decreasing
The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.
Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing.
Find the intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
Show that y = `log(1+x) - (2x)/(2+x), x> - 1`, is an increasing function of x throughout its domain.
Prove that y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`
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)`
Let f be a function defined on [a, b] such that f '(x) > 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b).
Find the interval in which the following function are increasing or decreasing f(x) = x2 + 2x − 5 ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
Show that f(x) = tan−1 x − x is a decreasing function on R ?
Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?
What are the values of 'a' for which f(x) = ax is increasing on R ?
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
Let ϕ(x) = f(x) + f(2a − x) and f"(x) > 0 for all x ∈ [0, a]. Then, ϕ (x)
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
If the function f(x) = x3 − 9kx2 + 27x + 30 is increasing on R, then
The total cost of manufacturing x articles is C = 47x + 300x2 − x4. Find x, for which average cost is increasing.
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Choose the correct option from the given alternatives :
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly decreasing in ______.
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
Find the values of x for which the function f(x) = x3 – 6x2 – 36x + 7 is strictly increasing
Choose the correct alternative:
The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
A man of height 1.9 m walks directly away from a lamp of height 4.75m on a level road at 6m/s. The rate at which the length of his shadow is increasing is
For every value of x, the function f(x) = `1/"a"^x`, a > 0 is ______.
If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.
Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R
The function f (x) = 2 – 3 x is ____________.
The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
The function `"f"("x") = "log" (1 + "x") - (2"x")/(2 + "x")` is increasing on ____________.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
If f(x) = x3 + 4x2 + λx + 1(λ ∈ R) is a monotonically decreasing function of x in the largest possible interval `(–2, (–2)/3)` then ______.
The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
If f(x) = x + cosx – a then ______.
y = log x satisfies for x > 1, the inequality ______.
If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.
Read the following passage:
|
The use of electric vehicles will curb air pollution in the long run. V(t) = `1/5 t^3 - 5/2 t^2 + 25t - 2` where t represents the time and t = 1, 2, 3, ...... corresponds to years 2001, 2002, 2003, ...... respectively. |
Based on the above information, answer the following questions:
- Can the above function be used to estimate number of vehicles in the year 2000? Justify. (2)
- Prove that the function V(t) is an increasing function. (2)
The function f(x) = sin4x + cos4x is an increasing function if ______.

