Advertisements
Advertisements
प्रश्न
The function f(x) = x9 + 3x7 + 64 is increasing on
पर्याय
R
(−∞, 0)
(0, ∞)
R0
उत्तर
R
\[f\left( x \right) = x^9 + 3 x^7 + 64\]
\[f'\left( x \right) = 9 x^8 + 21 x^6 > 0, \forall x \in R\]
\[\text { So, f(x) is increasing on R } .\]
APPEARS IN
संबंधित प्रश्न
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 the following functions are strictly increasing or decreasing:
−2x3 − 9x2 − 12x + 1
Find the intervals in which the function f given by `f(x) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.
Show that the function f(x) = 4x3 - 18x2 + 27x - 7 is always increasing on R.
Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R ?
Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function 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(x) = −2x3 − 9x2 − 12x + 1 ?
Find the interval in which the following function are increasing or decreasing f(x) = \[5 x^\frac{3}{2} - 3 x^\frac{5}{2}\] x > 0 ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 + 9x + 15 ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?
Find the intervals in which f(x) = (x + 2) e−x is increasing or decreasing ?
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) ?
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x \[\leq 2\pi\] ?
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
Show that the function f given by f(x) = tan–1 (sin x + cos x) is decreasing for all \[x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) .\]
The radius r of a right circular cylinder is increasing uniformly at the rate of 0·3 cm/s and its height h is decreasing at the rate of 0·4 cm/s. When r = 3·5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. \[\left[ \text{ Use } \pi = \frac{22}{7} \right]\]
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).
Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R.
Find MPC ( Marginal propensity to Consume ) and APC ( Average Propensity to Consume ) if the expenditure Ec of a person with income I is given as Ec = ( 0.0003 ) I2 + ( 0.075 ) I when I = 1000.
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the values of x for which Revenue is increasing.
Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function
Test whether the following function f(x) = 2 – 3x + 3x2 – x3, x ∈ R is increasing or decreasing
The values of k for which the function f(x) = kx3 – 6x2 + 12x + 11 may be increasing on R are ______.
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
y = x(x – 3)2 decreases for the values of x given by : ______.
The function f(x) = tanx – x ______.
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 ____________.
Show that function f(x) = tan x is increasing in `(0, π/2)`.
Let f(x) = `x/sqrt(a^2 + x^2) - (d - x)/sqrt(b^2 + (d - x)^2), x ∈ R` where a, b and d are non-zero real constants. Then ______.
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 interval in which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
Find the interval/s in which the function f : R `rightarrow` R defined by f(x) = xex, is increasing.
