Advertisements
Advertisements
Question
The total cost function for production of articles is given as C = 100 + 600x – 3x2, then the values of x for which the total cost is decreasing is ______
Advertisements
Solution
x >100
RELATED QUESTIONS
Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.
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 function `f(x) = x^4/4 - x^3 - 5x^2 + 24x + 12` is (a) strictly increasing, (b) strictly decreasing
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.
Find the interval in which the following function are increasing or decreasing f(x) = 5x3 − 15x2 − 120x + 3 ?
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4)?
Prove that the function f given by f(x) = x − [x] is increasing in (0, 1) ?
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
What are the values of 'a' for which f(x) = ax is decreasing on R ?
Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?
Let f(x) = x3 − 6x2 + 15x + 3. Then,
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
If the function f(x) = cos |x| − 2ax + b increases along the entire number scale, then
Find `dy/dx,if e^x+e^y=e^(x-y)`
The total cost of manufacturing x articles is C = 47x + 300x2 − x4. Find x, for which average cost is increasing.
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Solve the following:
Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.
State whether the following statement is True or False:
The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.
Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is
- Strictly increasing
- strictly decreasing
The function f(x) = sin x + 2x is ______
The function f(x) = tan-1 (sin x + cos x) is an increasing function in:
The function f: N → N, where
f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is
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 ______.
The interval in which the function f(x) = `(4x^2 + 1)/x` is decreasing is ______.
Read the following passage:
|
The use of electric vehicles will curb air pollution in the long run. V(t) = `1/5 t^3 - 5/2 t^2 + 25t - 2` where t represents the time and t = 1, 2, 3, ...... corresponds to years 2001, 2002, 2003, ...... respectively. |
Based on the above information, answer the following questions:
- Can the above function be used to estimate number of vehicles in the year 2000? Justify. (2)
- Prove that the function V(t) is an increasing function. (2)

