Mean value theorem Quiz 1

Question 1

Solve the question to find ‘$$c$$’ by using Rolle’s theorem for the function $${x^2} - 4$$on $$[ - 2,2]$$.

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$3$$

Answer

$$2$$

Question 2

Tick the correct answer for the value of $$c$$ by using Rolle’s theorem for the function as $${x^3} - 2{x^2} - x + 2$$ which exists in the interval of $$[ - 1,2]$$.

Accepted Answer

$$1.55, - 0.22$$

Answer

$$.55, - 0.55$$

Answer

$$1.55, - 0.32$$

Answer

$$ - 1.55, - 0.22$$

Question 3

Choose the correct option for the value of $$c$$for the function $${e^{9 - {x^2}}}$$ using Rolle’s theorem which exists in the interval $$[ - 3,3]$$.

Accepted Answer

$$0$$

Answer

$$3$$

Answer

$$4$$

Answer

$$1$$

Question 4

Tick the correct answer for the value of $$c$$ by using Lagrange's mean value theorem for the function as $$3x - {x^2}$$ which exists in the interval of $$[0,1]$$.

Accepted Answer

$$1$$

Answer

$$\dfrac{3}{2}$$

Answer

$$1\dfrac{3}{2}$$

Answer

$$\dfrac{7}{2}$$

Question 5

Choose the correct option for the value of $$c$$for the function $$x + \dfrac{1}{{2x}}$$using Lagrange's mean value theorem which exists in the interval $$[1,3]$$.

Accepted Answer

$$ \pm \sqrt 3 $$

Answer

$$5$$

Answer

$$ \pm \sqrt 2 $$

Answer

$$ \pm \sqrt 6 $$