Advertisements
Advertisements
Question
Find the value of x such that f(x) is decreasing function.
f(x) = x4 − 2x3 + 1
Advertisements
Solution
f(x) = x4 − 2x3 + 1
∴ f'(x) = 4x3 - 6x2 = 2x2 (2x - 3)
f(x) is a decreasing function, if f'(x) < 0
∴ 2x2 (2x - 3) < 0
As x2 is always positive,
(2x - 3) < 0
∴ 2x < 3
∴ x < `3/2`
Thus, f(x) is a decreasing function for x <`3/2`, i.e. `(- ∞, 3/2)`.
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 following functions are strictly increasing or decreasing:
−2x3 − 9x2 − 12x + 1
Show that y = `log(1+x) - (2x)/(2+x), x> - 1`, is an increasing function of x throughout its domain.
Prove that the logarithmic function is strictly increasing on (0, ∞).
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
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
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) = 10 − 6x − 2x2 ?
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) = 5x3 − 15x2 − 120x + 3 ?
Find the interval in which the following function are increasing or decreasing f(x) = (x − 1) (x − 2)2 ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \log\left( 2 + x \right) - \frac{2x}{2 + x}, x \in R\] ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Show that f(x) = e2x is increasing on R.
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Show that f(x) = tan−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?
State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
Prove that the following function is increasing on R f \[(x) =\]3 \[x^5\] + 40 \[x^3\] + 240\[x\] ?
Every invertible function is
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.
y = x(x – 3)2 decreases for the values of x given by : ______.
In case of decreasing functions, slope of tangent and hence derivative is ____________.
The function f(x) = tan-1 x is ____________.
Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.
If f(x) = x5 – 20x3 + 240x, then f(x) satisfies ______.
If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
