Advertisements
Advertisements
Question
y = x(x – 3)2 decreases for the values of x given by : ______.
Options
1 < x < 3
x < 0
x > 0
`0 < x < 3/2`
Solution
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
RELATED QUESTIONS
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
Show that the function `f(x) = x^3 - 3x^2 + 6x - 100` is increasing on R
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:
10 − 6x − 2x2
Prove that the logarithmic function is strictly increasing on (0, ∞).
Which of the following functions are strictly decreasing on `(0, pi/2)`?
- cos x
- cos 2x
- cos 3x
- tan x
Find the intervals in which the function f given by `f(x) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.
Find the intervals in which the function `f(x) = x^4/4 - x^3 - 5x^2 + 24x + 12` is (a) strictly increasing, (b) strictly decreasing
Show that f(x) = \[\frac{1}{1 + x^2}\] is neither increasing nor decreasing on R ?
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) = 6 + 12x + 3x2 − 2x3 ?
Find the interval in which the following function are increasing or decreasing f(x) = x8 + 6x2 ?
Prove that the following function is increasing on R f \[(x) =\]3 \[x^5\] + 40 \[x^3\] + 240\[x\] ?
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
The function f(x) = x9 + 3x7 + 64 is increasing on
Prove that the function f : N → N, defined by f(x) = x2 + x + 1 is one-one but not onto. Find the inverse of f: N → S, where S is range of f.
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
The total cost function for production of articles is given as C = 100 + 600x – 3x2, then the values of x for which the total cost is decreasing is ______
The function f(x) = 9 - x5 - x7 is decreasing for
Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.
The function f (x) = x2, for all real x, is ____________.
The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.
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))` = ______.
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
