Derivative definition and notation Quiz 1

Question 1

Statement 1: Differentiation of any constant is always a zero. $$ \ $$ Statement 2: For any function if the slope of the tangent is equal, then that function is the derivative of the same function. $$ \ $$ Which of the following is the correct option regarding the given statements?

Accepted Answer

Both statements are true

Answer

Statement 1 is correct

Answer

Statement 2 is correct

Answer

None of the above

Question 2

Which of the following option$$($$s$$)$$ is/are correct regarding the derivatives?

Accepted Answer

All of the above

Answer

Leibnitz’s differential equation is represented as $${{\left( \dfrac{d}{dx} \right)}^{n}}y\left( x \right)=\dfrac{{{d}^{n}}y}{d{{x}^{n}}}$$.

Answer

The derivative of function is represented by $${y}'$$ in Lagrange’s Notation.

Answer

The derivative of function is represented by $$\overset{.}{\mathop{y}}$$ in Newton’s Notation.

Question 3

Choose the correct option for the given function $$f\left( x \right)=\dfrac{99}{x}$$

Accepted Answer

$${f}'\left( x ight)=\underset{\Delta x	o 0}{\mathop{\lim }}\,\dfrac{-99}{x\left( x+\Delta x ight)}$$

Answer

$${f}'\left( x ight)=\underset{\Delta x	o 0}{\mathop{\lim }}\,\dfrac{99}{x\left( {{x}^{2}}+\Delta x ight)}$$

Answer

$${f}'\left( x ight)=\underset{\Delta x	o 0}{\mathop{\lim }}\,\dfrac{11}{x\left( x+\Delta x ight)}$$

Answer

$${f}'\left( x ight)=\underset{\Delta x	o 0}{\mathop{\lim }}\,\dfrac{99}{{{x}^{2}}\left( x+\Delta x ight)}$$

Question 4

If the derivation of the function $$f\left( x ight)=\dfrac{33}{2}\left( \sqrt{x} ight)$$ is $$\underset{\Delta x	o 0}{\mathop{\lim }}\,\dfrac{a}{b}\left( \dfrac{1}{\sqrt{x+\Delta x}+\sqrt{x}} ight)$$. Then find $$\dfrac{a}{b}$$?

Accepted Answer

$$\dfrac{33}{2}$$

Answer

$$\dfrac{33}{4}$$

Answer

$$\dfrac{66}{2}$$

Answer

$$\dfrac{68}{4}$$

Question 5

If the derivative of the function $$f\left( x ight)=	ext{ }8{{x}^{2}}-4x+9$$ with respect to $$x$$ is $$ax-b$$. Then find $$\sqrt{a}-b$$

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$12$$

Answer

$$1.3$$