Advertisements
Advertisements
प्रश्न
Function f(x) = x3 − 27x + 5 is monotonically increasing when ______.
विकल्प
x < −3
| x | > 3
x ≤ −3
| x | ≥ 3
Advertisements
उत्तर
Function f(x) = x3 − 27x + 5 is monotonically increasing when | x | > 3.
Explanation:
\[f\left( x \right) = x^3 - 27x + 5\]
\[f'\left( x \right) = 3 x^2 - 27\]
\[ = 3 \left( x^2 - 9 \right)\]
\[\text { For f(x) to be increasing, we must have }\]
\[f'\left( x \right) > 0\]
\[ \Rightarrow 3 \left( x^2 - 9 \right) > 0\]
\[ \Rightarrow \left( x^2 - 9 \right) > 0 \left[ \text { Since } 3 > 0, 3 \left( x^2 - 9 \right) > 0 \Rightarrow \left( x^2 - 9 \right) > 0| \right]\]
\[ \Rightarrow \left( x + 3 \right)\left( x - 3 \right) > 0\]
\[ \Rightarrow x < - 3 \ or \ x > 3\]
\[ \Rightarrow \left| x \right| > 3\]
APPEARS IN
संबंधित प्रश्न
Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
Prove that the function f given by f(x) = log cos x is strictly decreasing on `(0, pi/2)` and strictly increasing on `((3pi)/2, 2pi).`
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) = −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 \[f\left( x \right) = 3 x^4 - 4 x^3 - 12 x^2 + 5\] ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
Show that f(x) = sin x is an increasing function on (−π/2, π/2) ?
Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?
Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?
Write the set of values of 'a' for which f(x) = loga x is increasing in its domain ?
Write the set of values of a for which f(x) = cos x + a2 x + b is strictly increasing on R ?
The interval of increase of the function f(x) = x − ex + tan (2π/7) is
Let \[f\left( x \right) = \tan^{- 1} \left( g\left( x \right) \right),\],where g (x) is monotonically increasing for 0 < x < \[\frac{\pi}{2} .\] Then, f(x) is
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
Show that the function f given by f(x) = tan–1 (sin x + cos x) is decreasing for all \[x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) .\]
Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing.
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Solve the following : Find the intervals on which the function y = xx, (x > 0) is increasing and decreasing.
Find the value of x such that f(x) is decreasing function.
f(x) = x4 − 2x3 + 1
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.
Let f(x) = x3 − 6x2 + 9𝑥 + 18, then f(x) is strictly decreasing in ______
Show that the function f(x) = x3 + 10x + 7 for x ∈ R is strictly increasing
Find the values of x such that f(x) = 2x3 – 15x2 – 144x – 7 is decreasing function
f(x) = `{{:(0"," x = 0 ), (x - 3"," x > 0):}` The function f(x) is ______
Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.
In case of decreasing functions, slope of tangent and hence derivative is ____________.
The function f(x) = tan-1 x is ____________.
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 ______.
The function f(x) = sin4x + cos4x is an increasing function if ______.
Find the interval in which the function f(x) = x2e–x is strictly increasing or decreasing.
