Tag: to find the maximum profit if marginal revenue and marginal cost function are given:

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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 for x units of a commodity is given by $C(x)=\dfrac{x^3}{3}+x^2-15x+3$. Find marginal cost function.

  1. $x^2+2x-15$
  2. $x^2-2x-15$
  3. $x^2+2x+15$

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

$\Rightarrow$  We have, $C(x)=\dfrac{x^3}{3}+x^2-15x+3$.

$\Rightarrow$  Marginal cost = $\dfrac{d}{dx}(C)$

$\Rightarrow$  Marginal cost = $\dfrac{d}{dx}(\dfrac{x^3}{3}+x^2-15x+3)$

$\Rightarrow$  Marginal cost = $\dfrac{3\times x^2}{3}+2\times x-15$

$\therefore$    Marginal cost = $x^2+2x-15$

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

When we differentiate an expression with respect to one of a number of independent variables, we are engaged in

  1. Finding definite integrals

  2. Total differentiation

  3. Partial differentiation

  4. Integration
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant.

Hence, C is correct.

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 $C(x)=2x^2-4x+5$. Find the average cost when $x=2$.

  1. $\dfrac{5}{2}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{3}{4}$
  4. $\dfrac{5}{7}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have, $C(x)=2x^2-4x+5.$


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


$\Rightarrow$    Average cost = $\dfrac{2x^2-4x+5}{x}$

$\Rightarrow$    Average cost = $2x-4+\dfrac{5}{x}$

$\Rightarrow$    Now, substitute value of $x=2$.
$\Rightarrow$    Average cost = $2(2)-4+\dfrac{5}{2}=\dfrac{5}{2}$

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 $C(x)=2x^2-4x+5$. Find the average cost when $x=10$.

  1. $16.5$
  2. $15.5$
  3. $12.5$

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

$\Rightarrow$  We have, $C(x)=2x^2-4x+5$.

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

$\Rightarrow$  Average cost = $\dfrac{2x^2-4x+5}{x}$

$\Rightarrow$  Average cost = $2x-4+\dfrac{5}{x}$

$\Rightarrow$  Substitute value of $x=10$.
$\Rightarrow$  Average cost = $2\times 10-4+\dfrac{5}{10}=20-4+0.5=16.5$
$\therefore$  $ Average\, cost = 16.5$

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 $C(x)=4x^2-x+70$. Find the marginal cost when $x=3$.

  1. 23

  2. 24

  3. 25

  4. 26
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have, $C(x)=4x^2-x+70$.


$\Rightarrow$  Marginal cost = $\dfrac{d}{dx}C(x)$


$\Rightarrow$  Marginal cost = $\dfrac{d}{dx}(4x^2-x+70)$

$\Rightarrow$  Marginal cost = $2\times 4x-1=8x-1$
$\Rightarrow$  Substitute value of $x=3$,
$\Rightarrow$  Marginal cost = $8\times3-1=23$
$\therefore$    $Marginal\, cost = 23$.

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 $C(x)=2x^2-4x+5$. Find the marginal cost when $x=10$.

  1. 34

  2. 35

  3. 36

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

$\Rightarrow$   We have, $C(x)=2x^2-4x+5$.

$\Rightarrow$   Marginal cost = $\dfrac{d}{dx}C(x)$
$\Rightarrow$   Marginal cost = $\dfrac{d}{dx}(2x^2-4x+5)$
$\Rightarrow$   Marginal cost = $4x-4$
$\Rightarrow$   Now substitute value of $x=10$.
$\Rightarrow$   Marginal cost = $4(10)-4=40-4=36.$

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 $C(x)=2x^2-4x+5$. Find the marginal cost when $x=2$.

  1. 4

  2. 5

  3. 6

  4. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have, $C(x)=2x^2-4x+5$.


$\Rightarrow$  Marginal cost = $\dfrac{d}{dx}C(x)$.


$\Rightarrow$  Marginal cost = $\dfrac{d}{dx}(2x^2-4x+5)$

$\Rightarrow$  Marginal cost = $4x-4$
$\Rightarrow$  Substitute value of $x=2$.
$\Rightarrow$  Marginal cost = $4\times 2-4=8-4=4$
$\therefore$    $Marginal\,cost=4.$

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

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

  1. 19

  2. 18

  3. 16

  4. 17
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

$\Rightarrow$   Marginal cost = $\dfrac{d}{dx}C(x)$

$\Rightarrow$   Marginal cost = $\dfrac{d}{dx}(3x^2-2x+3)$

$\Rightarrow$   Marginal cost = $2\times 3x-2=6x-2$.
$\Rightarrow$   Now, substitute value of $x=3$,
$\Rightarrow$   Marginal cost = $6\times 3-2=18-2=16$

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 for x units of a commodity is given by $C(x)=3x^3-6x+5$. Find marginal cost function , when $x=2$.

  1. $6$
  2. $4$
  3. $2$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The derivative of the cost function $C(x)$ is called marginal cost with notation:

$C'(x)=  \dfrac{dC}{dx} $

$C'(x)=  9\times x^{2} -6 $

Putting the value of x as $2$

We get

$C'(x)=  9\times 2^{2} -6 $

$C'(x)=  30 $

$Marginal\space cost =36$