Advertisements
Advertisements
प्रश्न
Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.
Advertisements
उत्तर
f(x) = `3/"x" + 10`
For function to be decreasing, f '(x) < 0
Then f '(x) = `(- 3)/"x"^2 < 0` ....[∵ x ≠ 0, - x2 < 0]
Negative sign indicates that it always decreases as x2 never becomes negative.
Thus, f(x) is a decreasing function for x ≠ 0.
APPEARS IN
संबंधित प्रश्न
The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?
The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.
(A) increasing
(B) decreasing
(C) increasing and decreasing
(D) neither increasing nor decreasing
Show that the function given by f(x) = 3x + 17 is strictly increasing on R.
Prove that y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`
Let f be a function defined on [a, b] such that f '(x) > 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b).
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) = x3 − 12x2 + 36x + 17 ?
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
Show that the function f given by f(x) = 10x is increasing for all x ?
Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?
Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
Find the intervals in which function f given by f(x) = 4x3 - 6x2 - 72x + 30 is (a) strictly increasing, (b) strictly decresing .
Find the value of x, such that f(x) is increasing function.
f(x) = x2 + 2x - 5
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 – 15x2 – 84x – 7
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
A man of height 1.9 m walks directly away from a lamp of height 4.75m on a level road at 6m/s. The rate at which the length of his shadow is increasing is
The function f(x) = 9 - x5 - x7 is decreasing for
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is
If f(x) = x3 + 4x2 + λx + 1(λ ∈ R) is a monotonically decreasing function of x in the largest possible interval `(–2, (–2)/3)` then ______.
If f(x) = x + cosx – a then ______.
As one moves from left to right on a graph, what does a decrease in the \[y\]-values indicate?
For \[f(x)=x^3-3x^2+4x\], what is \[f'(x)\]?
