Advertisements
Advertisements
प्रश्न
y = x(x – 3)2 decreases for the values of x given by : ______.
विकल्प
1 < x < 3
x < 0
x > 0
`0 < x < 3/2`
उत्तर
y = x(x – 3)2 decreases for the values of x given by : 1 < x < 3.
Explanation:
Here y = x(x – 3)2
`"dy"/"dx" = x * 2(x - 3) + (x - 3)^2 * 1`
⇒ `"dy"/"dx" = 2x(x - 3) + (x - 3)^2`
For increasing and decreasing `"dy"/"dx"` = 0
∴ 2x(x – 3) + (x – 3)2 = 0
⇒ (x – 3)(2x + x – 3) = 0
⇒ (x – 3)(3x – 3) = 0
⇒ 3(x – 3)(x – 1) = 0
∴ x = 1, 3
∴ Possible intervals are `(– oo, 1), (1, 3), (3, oo)`
`"dy"/"dx"` = (x – 3)(x – 1)
For `(– oo, 1)` = (–) (–) = (+) increasing
For (1, 3) = (–) (+) = (–) decreasing
For `(3, oo)` = (+) (+) = (+) increasing
So the function decreases in (1, 3) or 1 < x < 3
APPEARS IN
संबंधित प्रश्न
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)`
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.
Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?
Without using the derivative show that the function f (x) = 7x − 3 is strictly increasing function on R ?
Find the interval in which the following function are increasing or decreasing f(x) = 5x3 − 15x2 − 120x + 3 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 + 9x2 + 12x + 20 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 9x2 + 12x − 5 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 24x + 107 ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x3 + 4x2 + 15 ?
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
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 f(x) = loga x is decreasing in its domain ?
Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?
Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?
f(x) = 2x − tan−1 x − log \[\left\{ x + \sqrt{x^2 + 1} \right\}\] is monotonically increasing when
If the function f(x) = cos |x| − 2ax + b increases along the entire number scale, then
The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if
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.
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
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
State whether the following statement is True or False:
If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1
For every value of x, the function f(x) = `1/7^x` is ______
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.
Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
The length of the longest interval, in which the function `3 "sin x" - 4 "sin"^3"x"` is increasing, is ____________.
State whether the following statement is true or false.
If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
