Advertisements
Advertisements
प्रश्न
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
Advertisements
उत्तर
Price function P is given by
`"P" = 183 + 120"D" - 3"D"^2`
Differentiating w.r.t. D
`"dP"/"dD"=120-6D`
If price is increasing then we have `"dP"/"dD">0`
∴ 120 - 6D > 0
∴ 6D < 120
∴ D < 20
∴ The price is increasing for D < 20.
APPEARS IN
संबंधित प्रश्न
Find the intervals in which the function f(x) = 3x4 − 4x3 − 12x2 + 5 is
(a) strictly increasing
(b) strictly decreasing
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 ?
Find the value of c in Rolle's theorem for the function `f(x) = x^3 - 3x " in " (-sqrt3, 0)`
Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
Prove that the logarithmic function is strictly increasing on (0, ∞).
Let I be any interval disjoint from (−1, 1). Prove that the function f given by `f(x) = x + 1/x` is strictly increasing on I.
Find the intervals in which the function f given by `f(x) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.
Prove that the function f(x) = loga x is increasing on (0, ∞) if a > 1 and decreasing on (0, ∞), if 0 < a < 1 ?
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) = −2x3 − 9x2 − 12x + 1 ?
Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
Prove that the function f given by f(x) = x − [x] is increasing in (0, 1) ?
Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x \[\leq 2\pi\] ?
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) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval
Function f(x) = loga x is increasing on R, if
Prove that the function `f(x) = x^3- 6x^2 + 12x+5` is increasing on R.
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 + 36x + 1
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
If f(x) = [x], where [x] is the greatest integer not greater than x, then f'(1') = ______.
If f(x) = x3 – 15x2 + 84x – 17, then ______.
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
The function `"f"("x") = "x"/"logx"` increases on the interval
Function f(x) = `log(1 + x) - (2x)/(2 + x)` is monotonically increasing when ______.
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
