Advertisements
Advertisements
प्रश्न
The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.
Advertisements
उत्तर
Let x be the edge of the cube and V be its volume at any time t.
Then V = x3
Differentiating both sides w.r.t. t, we get
`"dV"/"dt" = 3x^2"dx"/"dt"`
Now, `dx/dt = (0.6"cm")/sec` and x = 2 cm
∴ `"dV"/dt` = 3(2)2(0.6)
= 7.2
Hence, the volume of the cube is decreasing at the rate of `(7.2"cm"^3)/sec`.
APPEARS IN
संबंधित प्रश्न
The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.
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
Find the least value of a such that the function f given by f (x) = x2 + ax + 1 is strictly increasing on [1, 2].
Without using the derivative, show that the function f (x) = | x | is.
(a) strictly increasing in (0, ∞)
(b) strictly decreasing in (−∞, 0) .
Find the interval in which the following function are increasing or decreasing f(x) = 6 − 9x − x2 ?
Find the interval in which the following function are increasing or decreasing f(x) = 5 + 36x + 3x2 − 2x3 ?
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 \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?
Determine the values of x for which the function f(x) = x2 − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x2 − 6x + 9 where the normal is parallel to the line y = x + 5 ?
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) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
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 function f given by f(x) = x − [x] is increasing in (0, 1) ?
Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
The function f(x) = cot−1 x + x increases in the interval
The function f(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval
The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if
Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.
show that f(x) = `3x + (1)/(3x)` is increasing in `(1/3, 1)` and decreasing in `(1/9, 1/3)`.
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Test whether the function f(x) = x3 + 6x2 + 12x − 5 is increasing or decreasing for all x ∈ R
The slope of tangent at any point (a, b) is also called as ______.
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
Find the values of x such that f(x) = 2x3 – 15x2 – 144x – 7 is decreasing function
A circular pIate is contracting at the uniform rate of 5cm/sec. The rate at which the perimeter is decreasing when the radius of the circle is 10 cm Jong is
The area of the square increases at the rate of 0.5 cm2/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.
If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.
A ladder 20 ft Jong leans against a vertical wall. The top-end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is ______
Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R
The interval on which the function f(x) = 2x3 + 9x2 + 12x – 1 is decreasing is ______.
The function f(x) = tanx – x ______.
The function `"f"("x") = "log" (1 + "x") - (2"x")/(2 + "x")` is increasing on ____________.
Let h(x) = f(x) - [f(x)]2 + [f(x)]3 for every real number x. Then ____________.
The function f: N → N, where
f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is
Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.
Let f: [0, 2]→R be a twice differentiable function such that f"(x) > 0, for all x ∈( 0, 2). If `phi` (x) = f(x) + f(2 – x), then `phi` is ______.
Let f(x) = tan–1`phi`(x), where `phi`(x) is monotonically increasing for `0 < x < π/2`. Then f(x) is ______.
y = log x satisfies for x > 1, the inequality ______.
The function f(x) = tan–1(sin x + cos x) is an increasing function in ______.
If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.
Find the interval/s in which the function f : R `rightarrow` R defined by f(x) = xex, is increasing.
The function f(x) = sin4x + cos4x is an increasing function if ______.
Let \[x_0\] be in the domain of a real-valued function \[f\]. When is \[f\] decreasing at \[x_0\]?
For \[f'(x)=12(x-3)(x+2)\], what are the critical points obtained from \[f'(x)=0\]?
