Advertisements
Advertisements
प्रश्न
The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.
(A) increasing
(B) decreasing
(C) increasing and decreasing
(D) neither increasing nor decreasing
Advertisements
उत्तर
(A) increasing
`f(x)=x^3-3x^2+3x-100, x in R`
`f'(x)=3x^2-6x+3`
`=3(x^2-2x+1)`
`=3(x-1)^2`
Since, (x – 1)2 is always positive x ≠ 1
f'(x) > 0 for all x ∈ R, x ≠ 1
Hence, f (x) is an increasing function, for all x ∈ R, x ≠ 1
APPEARS IN
संबंधित प्रश्न
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
Find the intervals in which the function f given by f(x) = 2x2 − 3x is
- strictly increasing
- strictly decreasing
Find the intervals in which the following functions are strictly increasing or decreasing:
10 − 6x − 2x2
Find the values of x for `y = [x(x - 2)]^2` is an increasing function.
The interval in which y = x2 e–x is increasing is ______.
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 24x + 7 ?
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) ?
Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4)?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
Write the set of values of a for which f(x) = cos x + a2 x + b is strictly increasing on R ?
The function f(x) = xx decreases on the interval
The function \[f\left( x \right) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right)\] is of the following types:
Function f(x) = cos x − 2 λ x is monotonic decreasing when
Function f(x) = x3 − 27x + 5 is monotonically increasing when ______.
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
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.
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Choose the correct alternative.
The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
If f(x) = `x^(3/2) (3x - 10)`, x ≥ 0, then f(x) is increasing in ______.
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
The function f(x) = 4 sin3x – 6 sin2x + 12 sinx + 100 is strictly ______.
Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.
The function f (x) = 2 – 3 x is ____________.
The function f (x) = x2, for all real x, is ____________.
In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.
If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:
Which of the following graph represent the strictly increasing function.
The function f(x) = `(4x^3 - 3x^2)/6 - 2sinx + (2x - 1)cosx` ______.
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly increasing in ______.
Find the interval in which the function f(x) = x2e–x is strictly increasing or decreasing.
The function \[f(x)=x^3-3x^2+4x\], \[x\in\mathbf{R}\], is
The critical points \[x=-2\] and \[x=3\] divide the real line into which three intervals?
For \[f'(x)=12(x-3)(x+2)\], what is the nature of \[f\] on \[(-2,3)\]?
