Advertisements
Advertisements
प्रश्न
For manufacturing x units, labour cost is 150 – 54x and processing cost is x2. Price of each unit is p = 10800 – 4x2. Find the value of x for which Total cost is decreasing.
Advertisements
उत्तर
Total cost C(x) = Processing cost + labour cost
C(x) = x2 + 150 - 54x
C(x) = x2 - 54x + 150
`("dc")/("dx")` = 2x - 54
Total cost is decreasing
If `("dc")/("dx")`< 0
i.e if 2x - 54 < 0
i.e if 2x < 54
i.e if x < 27
Total cost C is decreasing for x < 27.
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 intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
Water is dripping out from a conical funnel of semi-verticle angle `pi/4` at the uniform rate of `2 cm^2/sec`in the surface, through a tiny hole at the vertex of the bottom. When the slant height of the water level is 4 cm, find the rate of decrease of the slant height of the water.
Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R ?
Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x ?
Show that f(x) = cos2 x is a decreasing function on (0, π/2) ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
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) = sinx(1 + cosx), 0 < x < \[\frac{\pi}{2}\] ?
The function f(x) = xx decreases on the interval
The function f(x) = x2 e−x is monotonic increasing when
Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x2 – x3, x ∈ R.
Find the values of x for which the following functions are strictly increasing : f(x) = 2x3 – 3x2 – 12x + 6
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Find the value of x, such that f(x) is increasing function.
f(x) = x2 + 2x - 5
Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function
If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______
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 ______.
The function f(x) = x3 - 3x is ______.
Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`
Show that f(x) = tan–1(sinx + cosx) is an increasing function in `(0, pi/4)`
Which of the following functions is decreasing on `(0, pi/2)`?
The function f (x) = x2, for all real x, is ____________.
The function `"f"("x") = "x"/"logx"` increases on the interval
Let 'a' be a real number such that the function f(x) = ax2 + 6x – 15, x ∈ R is increasing in `(-∞, 3/4)` and decreasing in `(3/4, ∞)`. Then the function g(x) = ax2 – 6x + 15, x∈R has a ______.
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 ______.
A function f is said to be increasing at a point c if ______.
The function f(x) = xex(1 − x), x ∈ R, is ______.
