Tag: applications of calculus

Quizzes (3) Questions (43)

Questions Related to applications of calculus

Multiple choice business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

The cost function of a firm $C(x)=3x^2-2x+3$. Find the average cost when $x=3$.

  1. 8

  2. 9

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have, $C(x)=3x^2-2x+3$

$\Rightarrow$  Average cost = $\dfrac{C(x)}{x}$

$\Rightarrow$  Average cost = $\dfrac{3x^2-2x+3}{x}$

$\Rightarrow$  Average cost = $3x-2+\dfrac{3}{x}$.

$\Rightarrow$  Substitute value of $x=3$,
$\Rightarrow$  Average cost = $3\times 3-2+\dfrac{3}{3}=9-2+1=8$
$\therefore$    $Average\, cost\,=8$. 

Multiple choice business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

If the demanding Law is given by $q = \dfrac{20}{p+1}$, find the elasticity of demand with respect to price at the point when $p = 3.$

  1. $\dfrac43$
  2. $-\dfrac34$
  3. $\dfrac23$
  4. $-\dfrac32$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Elasticity of demand $=\cfrac{\cfrac{dq}{q}}{\cfrac{dp}{p}}=-\cfrac{p}{(p+1)}$
When $p=3$
Elasticity of demand $=-\cfrac{3}{4}$
Multiple choice business mathematics and statistics applications of calculus marginal income and marginal cost to find the maximum profit if marginal revenue and marginal cost function are given: integral calculus – ii

If the total cost function for a manufacturer is given by $C =\dfrac{5x^2}{\sqrt(x^2+3)}+5000$, find marginal cost function.

  1. $\dfrac{3x(x^2+6)}{(x^2+3)^{(3/2)}}$
  2. $\dfrac{4x(x^2+6)}{(x^2+3)^{(3/2)}}$
  3. $\dfrac{5x(x^2+6)}{(x^2+3)^{(3/2)}}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given cost function $C\left(x\right)=\dfrac{5x^2}{\sqrt{\left(x^2+3\right)}}+5000$


Marginal cost function is given by $C'\left(x\right)$

$C'\left(x\right)=\dfrac{\left(\sqrt{x^2+3}\right)\left(10x\right)-\dfrac{5x^2}{2\sqrt{x^2+3}}\times\left({2x+10}\right)}{\left(\sqrt{x^2+3}\right)^2}$

$\dfrac{d}{dx}\left(\dfrac{u}{v}\right)=\dfrac{v\dfrac{du}{dx}-u\dfrac{dv}{dx}}{v^2}$

$C'\left(x\right)=\dfrac{2\left(x^2+3\right)\left(10x\right)-5x^2\left(2x\right)}{2\left(\sqrt{x^2+3}\right)^3}=\dfrac{5x\left(x^2+6\right)}{\left(x^2+3\right)^\tfrac{3}{2}}$