Advertisements
Advertisements
प्रश्न
The cost C of producing x articles is given as C = x3-16x2 + 47x. For what values of x, with the average cost is decreasing'?
उत्तर
C = x3 - 16x2 + 47x.
Average cost CA = `"C"/"x" = ("x"^3 - 16"x"^2 + 47"x")/"x"`
∴ CA = x2 - 16x + 47
Differentiating w.r.t. x
`"dC"_"A"/"dx" = 2"x" - 16`
CA is decreasing if `"dC"_"A"/"dx" < 0`
i.e. 2x - 16 < 0
i.e. 2x < 16
i.e. x < 8
∴ Average cost CA is decreasing for x < 8.
APPEARS IN
संबंधित प्रश्न
If `log_10((x^3-y^3)/(x^3+y^3))=2 "then show that" dy/dx = [-99x^2]/[101y^2]`
If x=at2, y= 2at , then find dy/dx.
If `ax^2+2hxy+by^2=0` , show that `(d^2y)/(dx^2)=0`
If y =1 - cos θ , x = 1 - sin θ , then ` dy/dx at " "θ =pi/4` is ________
If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`
If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t) then find `dy/dx `
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx`
`x = 2at^2, y = at^4`
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a cos θ, y = b cos θ
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
x = a (θ – sin θ), y = a (1 + cos θ)
If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`
`x = (sin^3t)/sqrt(cos 2t), y = (cos^3t)/sqrt(cos 2t)`
If `x = sqrt(a^(sin^(-1)))`, y = `sqrt(a^(cos^(-1)))` show that `dy/dx = - y/x`
IF `y = e^(sin-1x) and z =e^(-cos-1x),` prove that `dy/dz = e^x//2`
Evaluate : `int (sec^2 x)/(tan^2 x + 4)` dx
x = `"e"^theta (theta + 1/theta)`, y= `"e"^-theta (theta - 1/theta)`
sin x = `(2"t")/(1 + "t"^2)`, tan y = `(2"t")/(1 - "t"^2)`
If x = 3sint – sin 3t, y = 3cost – cos 3t, find `"dy"/"dx"` at t = `pi/3`
If x = sint and y = sin pt, prove that `(1 - x^2) ("d"^2"y")/("dx"^2) - x "dy"/"dx" + "p"^2y` = 0
If `"x = a sin" theta "and y = b cos" theta, "then" ("d"^2 "y")/"dx"^2` is equal to ____________.
