The total cost C (x) in Rupees associated with the production of x units of an item is given by
C(X) = 0.007 x3 - 0.003x2 + 15x + 4000
Find the marginal cost when 17 units are produced.
Marginal cost is the rate of change of total cost with respect to output.
∴Marginal cost
\begin{align}MC=\frac{dC}{dx}=0.007 (3x^2) - 0.003(2x) + 15\end{align}
MC = 0.021 x2 - 0.006x + 15
When x = 17, MC = 0.021 (172) − 0.006 (17) + 15
= 0.021(289) − 0.006(17) + 15
= 6.069 − 0.102 + 15
= 20.967
Hence, when 17 units are produced, the marginal cost is Rs. 20.967.
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
(i) f : R → R defined by f(x) = 3 – 4x
(ii) f : R → R defined by f(x) = 1 + x2
Show that the Modulus Function f : R → R, given by f(x) = |x|, is neither oneone nor onto, where | x | is x, if x is positive or 0 and |x| is – x, if x is negative.
Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.
The order of the differential equation
\begin{align}2x^2\frac{d^2y}{dx^2}\;- \;3\frac{dy}{dx}\;+ y=\;0\end{align}
is (A) 2 (B) 1 (C) 0 (D) not defined
Classify the following as scalar and vector quantities.
(i) time period (ii) distance (iii) force
(iv) velocity (v) work done
Letbe a function defined as. The inverse of f is map g: Range
(A)
(B)
(C)
(D)
Consider f : R+ → [– 5, ∞) given by f(x) = 9x2 + 6x – 5. Show that f is invertible
with .
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.
Determine order and degree(if defined) of differential equation ym + 2yn + y' =0
Consider f : R+ → [4, ∞) given by f(x) = x2 + 4. Show that f is invertible with the inverse f–1 of f given by , where R+ is the set of all non-negative real numbers.