Advertisements
Advertisements
Question
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.
Solution
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval `(1, oo)`.
Explanation:
We have f(x) = `(2x^2 - 1)/x^4`
f'(x) = `(x^4(4x) - (2x^2 - 1) * 4x^3)/x^8`
⇒ f'(x) = `(4x^5 - (2x^2 - 1) * 4x^3)/x^8`
= `(4x^3[x^2 - 2x^2 + 1])/x^8`
= `(4(-x^2 + 1))/x^5`
For decreasing the function f'(x) < 0
∴ `(4(-x^2 + 1))/x^5 < 0`
⇒ `-x^2 + 1 < 0`
⇒ x2 < 1
∴ x > ± 1
⇒ `x ∈ (1, oo)`
Hence, the required interval is `(1, oo)`
APPEARS IN
RELATED QUESTIONS
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
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 given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
Find the intervals in which the function f given by `f(x) = (4sin x - 2x - x cos x)/(2 + cos x)` is (i) increasing (ii) decreasing.
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) = 2x3 − 15x2 + 36x + 1 ?
Find the interval in which the following function are increasing or decreasing f(x) = 6 + 12x + 3x2 − 2x3 ?
Show that f(x) = tan−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
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 ?
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.
Solve the following:
Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.
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.
State whether the following statement is True or False:
The function f(x) = `3/x` + 10, x ≠ 0 is decreasing
State whether the following statement is True or False:
If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
The function f(x) = x3 - 3x is ______.
If f(x) = `x^(3/2) (3x - 10)`, x ≥ 0, then f(x) is increasing in ______.
Show that f(x) = tan–1(sinx + cosx) is an increasing function in `(0, pi/4)`
The function f(x) = tan-1 x is ____________.
The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.
Which of the following graph represent the strictly increasing function.
Function given by f(x) = sin x is strictly increasing in.
Show that function f(x) = tan x is increasing in `(0, π/2)`.
The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
