Advertisements
Advertisements
प्रश्न
Find the value(s) of a for which f(x) = x3 − ax is an increasing function on R ?
Advertisements
उत्तर
\[f\left( x \right) = x^3 - ax\]
\[f'\left( x \right) = 3 x^2 - a\]
\[\text { Given }:f\left( x \right)\text { is increasing on R }.\]
\[ \Rightarrow f'\left( x \right) \geq 0 \forall x \in R\]
\[ \Rightarrow 3 x^2 - a \geq 0 \forall x \in R\]
\[ \Rightarrow a \leq 3 x^2 \forall x \in R\]
\[\text { The least value of } 3 x^2 \text { is } 0.\]
\[\therefore a \leq 0\]
APPEARS IN
संबंधित प्रश्न
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
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:
x2 + 2x − 5
Find the intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
Which of the following functions are strictly decreasing on `(0, pi/2)`?
- cos x
- cos 2x
- cos 3x
- tan x
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
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) ?
Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?
f(x) = 2x − tan−1 x − log \[\left\{ x + \sqrt{x^2 + 1} \right\}\] is monotonically increasing when
Function f(x) = loga x is increasing on R, if
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function
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
Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is
- Strictly increasing
- strictly 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 ______.
The slope of tangent at any point (a, b) is also called as ______.
f(x) = `{{:(0"," x = 0 ), (x - 3"," x > 0):}` The function f(x) is ______
For which interval the given function f(x) = 2x3 – 9x2 + 12x + 7 is increasing?
y = x(x – 3)2 decreases for the values of x given by : ______.
The function f(x) = tanx – x ______.
The function f (x) = 2 – 3 x is ____________.
The function f(x) = mx + c where m, c are constants, is a strict decreasing function for all `"x" in "R"` , if ____________.
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
If f(x) = x + cosx – a then ______.
Let f : R `rightarrow` R be a positive increasing function with `lim_(x rightarrow ∞) (f(3x))/(f(x))` = 1 then `lim_(x rightarrow ∞) (f(2x))/(f(x))` = ______.
A function f is said to be increasing at a point c if ______.
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
As one moves from left to right on a graph, what does a decrease in the \[y\]-values indicate?
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 \[(-2,3)\]?
For \[f(x)=4x^3-6x^2-72x+30\], on which intervals is \[f\] increasing?
