Sample QuestionsDIFFERENTIATION 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 formula for elasticity of demand ?
- ✓
– $\frac{p}{x} \cdot \frac{d x}{d p}$
- B
$\frac{p}{x} \cdot \frac{d x}{d p}$
- C
– $\frac{x}{p} \cdot \frac{d p}{d x}$
- D
$\frac{p}{x} \cdot \frac{d p}{d x}$
Answer: A.
View full solution →What are the necessary and sufficient conditions for a function to be minimum at $x=a$ ?
- A
$f^{\prime}(a)<0, f^{\prime \prime}(a)>0$
- ✓
$f^{\prime}(a)=0, f^{\prime \prime}(a)>0$
- C
$f^{\prime}(a)>0, f^{\prime}(a)>0$
- D
$f^{\prime}(a)=0 . f^{\prime \prime}(a)<0$
Answer: B.
View full solution →If the function $f(x)$ is increasing at $x=a$, then which is the correct option from the following ?
- ✓
$f^{\prime \prime}(a)>0$
- B
$f^{\prime}(a)=0$
- C
$f^{\prime}(a)=0$
- D
$f^{\prime}(a)<0$
Answer: A.
View full solution →If $u$ and $v$ are functions of $x.$ then what is the formula of derivative of $\frac{v}{u}\ ?$
- A
$\frac{v \cdot \frac{d u}{d x}-u \cdot \frac{d v}{d x}}{v^{2}}$
- B
$\frac{v \cdot \frac{d u}{d x}+u \cdot \frac{d v}{d x}}{v^{2}}$
- C
$\frac{u \cdot \frac{d v}{d x}+v \cdot \frac{d u}{d x}}{u^{2}}$
- ✓
$\frac{u \cdot \frac{d v}{d x}-v \cdot \frac{d u}{d x}}{u^{2}}$
Answer: D.
View full solution →If $u$ and $v$ are two functions of $x,$ then what is the formula of derivative of their product $?$
- A
$u \cdot \frac{d u}{d x}+v \cdot \frac{d v}{d x}$
- B
$u \cdot \frac{d v}{d x}-v \cdot \frac{d u}{d x}$
- C
$\frac{d u}{d x} \times \frac{d v}{d x}$
- ✓
$u \cdot \frac{d v}{d x}+v \cdot \frac{d u}{d x}$
Answer: D.
View full solution →View full solution →What is marginal revenue?
What are the stationery points of a function?
How will be the second order derivative of a function at $x=a$ if function is maximum at $x = a?$
View full solution →How will be the first order derivation of a function at $x= a$ if function is decreasing at $x=a?$
View full solution →If $y=\left(2 x^{2}+3\right)(3 x-2)$ then find derivative of $y$ with respect to $x$.
View full solution →Find $\frac{d y}{d x}$ for $y=x^{4}-3 x^{2}+2 x-3$
View full solution →Obtain derivative of $f(x)=k \quad(k$ is constant) with the help of definition.
View full solution →The cost function of a commodity is $C=5 x^{2}+6 x+2000$, where $x$ is the number of units produced. Find marginal cost when production is $\mathbf{5 0}$ units.
View full solution →If the demand function of pizza is $p=150-4 x$ then find the marginal revenue when demand is of $3$ pizzas and interpret it.
View full solution →Find $\frac{d y}{d x}$ for $y=x^{3}+\sqrt{x}-\frac{4}{x}+\frac{1}{\sqrt[3]{x}}+\frac{1}{4}$.
View full solution →Obtain derivative of $f(x)=\frac{1}{x}$ with the help of definition.
View full solution →The demand function of a commodity is $p=12-\sqrt{x}$. Find the elasticity of demand when the price is $9$ units and interpret it.
View full solution →Obtain derivative of $f(x)=x^{n}$ with the help of definition.
View full solution →If the demand function of a commodity is $x=\frac{50-p}{2}$ then find the marginal revenue when price is $₹ 30$.
View full solution →Obtain derivative of $f(x)=\sqrt{x}$ with the help of definition.
View full solution →If the production cost function for a producer is $C=100+0.015 x^{2}$ and revenue function is $R=3 x$ then find the profit function. How many units should be produced by the producer for maximum profit ?
View full solution →A factory produces $x$ units and its production capacity is $60,000$ units per day. Its daily total production cost is $C=250000+0.08 x+\frac{200000000}{x}$. How many units should be produced for minimum production cost $?$
View full solution →The daily cost of production for $x$ tons of a commodity is $10 x^{2}-1000 x+50000$. How many units should be produced for the minimum cost ? Also find the minimum cost.
View full solution →The demand function of a commodity is $x=50-4 p$. Find elasticity of demand when price is $p=5$ and interpret it.
View full solution →The demand function of a watch is $p=6000-2 x$. Find the demand which maximizes the revenue and also find the corresponding price.
View full solution →Find the maximum and minimum values of $y=x^{3}-2 x^{2}-4 x-1$.
View full solution →Find the maximum and minimum values of $f(x)=2 x^{3}+3 x^{2}-12 x-4$
View full solution →A toy is sold at $Rs. 20 $ Total cost of producing $x$ such toys is $C=1000+16.5 x+$ $0.001 x^{2}$ rupees. How many toys should be produced for maximum profit ?
View full solution →The selling price of a refrigerator as determined by the company is $Rs.10000 .$ The total cost of the production for $x$ refrigerator is $C=0.1 x^{2}+9000 x+100$ rupees. How many refrigerators should be manufactured for maximum profit ?
View full solution →