Sample QuestionsPART 2 : DIFFERENTIATION questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
What is the derivative of $y=x^5+\frac{1}{5}$ ?
- ✓
$5 x^4$
- B
$x^5+\frac{1}{5}$
- C
$5 x^4+5$
- D
$x^5-\frac{1}{5}$
Answer: A.
View full solution →What is $\frac{d y}{d x}$ if $y=\frac{1}{\sqrt[3]{x}}$ ?
Answer: C.
View full solution →If the profit function $=P$, revenue function $=R$ and cost function $=C$ then what is the profit function?
- A
$R=P-C$
- B
$P=C-R$
- C
$C=R+P$
- ✓
$P=R-C$
Answer: D.
View full solution →If the revenue function is $R=7 x ($where, $x=$ demand$),$ what is the unit price of the commodity?
- ✓
$7$
- B
$0$
- C
$1$
- D
Can be any positive number
Answer: A.
View full solution →The total cost function of producing $x$ units is $C=5 x^2+100$. What is the marginal cost for $10$ units ?
Answer: B.
View full solution →What is $\frac{d y}{d x}$ if $f(x)=\sqrt{x^5}$ ?
View full solution →Find $f^{\prime}(x)$ at $x=2$ if $f(x)=5 x^2-3$.
View full solution →What is $f^{\prime}(x)$ if $f(x)=\frac{x^3}{3}$ ?
View full solution →What is the value of $\frac{d^2 y}{d x^2}$ if $y=x$ ?
View full solution →What do you say for the derivative of the first derivative of a function?
Find $\frac{d^2 y}{d x^2}$ if $y=\left(x^{-2}\right)^{-1}$.
View full solution →If the total cost of producing $x$ units is $1.5 x^2-15
x+900$ then for which value of $x$, the marginal cost is zero?
View full solution →Obtain marginal revenue function if the demand function
is $p=10-3 x$.
View full solution →Find $\frac{d^2 y}{d x^2}$ if $y=\frac{1}{x^{\frac{1}{3}}}$.
View full solution →For which value of $x, f^{\prime}(x)=f(x)$ if $f(x)=\sqrt{x}$ ?
View full solution →The demand function is $p=50-4 x$. Find elasticity of demand at $x=10$.
View full solution →If total cost of $x$ units is $C=x^{\frac{3}{2}}+10 x+500$
then find marginal cost at $x=100$ and then interpret it too.
View full solution →If the demand function is $x=50-3 p$, find marginal
revenue at $x=10$.
View full solution →Find stationary point for $f(x)=8 x^2-4 x+17$.
View full solution →Determine whether a function $y=\sqrt{x}+\frac{1}
{\sqrt{x}}$ is increasing or decreasing at $x=2$.
View full solution →The profit function is $11 x-\frac{11 x^2}{20}-30$. How
many units should be produced to get the maximum profit?
View full solution →The demand function of a commodity is $p=\frac{675-
x^2}{10}$. Obtain the maximum revenue from it. Also
find the price of the commodity when revenue is maximum.
View full solution →The cost of producing $x$ tons of steel rods in a factory
is $C=5 x^2-100 x+100000$.
Find the production for minimum cost. Also find the
minimum cost
View full solution →The cost of producing $x$ tons of steel rods in a factory is $C=5 x^2-100 x+100000$.
View full solution →Define the minimum value of a function and state its
necessary and sufficient conditions.
The demand function of a commodity is $x=75-\frac
{3 p}{5}$ and the total cost of producing $x$ units is
$\frac{x^2}{5}+13 x+1000$. Obtain the maximum profit.
View full solution →The total cost of manufacturing $x$ mobile phones for a
mobile making company is $\frac{x^2}{20}+4 x+30$.
If the demand function of mobile phone is
$(p=\frac{30-x}{2})$, where $p=$ price(in thousand rupees), how many mobile phones should be produced to earn maximum profit? What price should be fixed for the maximum profit ?
View full solution →During summer, a local potter makes one refrigerator in 5
thousand rupees using clay and other materials. The
demand function of such a refrigerator is $p=21-x$,
where $p=$ price (in thousand rupees) and $x=$
demand of refrigerator. How many refrigerators should
the potter make to get maximum profit? Also obtain
the maximum profit.
View full solution →Obtain the maximum and minimum values of a function
$f(x)=4 x+\frac{1}{x}-3$.
View full solution →Obtain the maximum and minimum values of a function
$y=x^3-3 x^2-45 x+12$.
View full solution →