Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
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) = | 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) = x4 − 4x ?
Show that f(x) = log sin x is increasing on (0, π/2) and decreasing on (π/2, π) ?
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Show that f(x) = sin x is an increasing function on (−π/2, π/2) ?
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
Prove that the function f given by f(x) = x − [x] is increasing in (0, 1) ?
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
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
f(x) = 2x − tan−1 x − log \[\left\{ x + \sqrt{x^2 + 1} \right\}\] is monotonically increasing when
The function \[f\left( x \right) = \frac{\lambda \sin x + 2 \cos x}{\sin x + \cos x}\] is increasing, if
If the function f(x) = x2 − kx + 5 is increasing on [2, 4], then
Find the values of x for which the following functions are strictly decreasing : f(x) = x3 – 9x2 + 24x + 12
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
Test whether the function f(x) = x3 + 6x2 + 12x − 5 is increasing or decreasing for all x ∈ R
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
State whether the following statement is True or False:
If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1
The function f(x) = 9 - x5 - x7 is decreasing for
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:
Let x0 be a point in the domain of definition of a real valued function `f` and there exists an open interval I = (x0 – h, ro + h) containing x0. Then which of the following statement is/ are true for the above statement.
Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
If \[f'(x)<0\] throughout an interval, then \[f\] is
