Intermediate value theorem Quiz 1

Question 1

Anil found a statement in a book that states as “A function $$f(x)$$ will have a root in the interval $$(3,4)$$ if $$f(3)$$ and $$f(4)$$ have opposite signs”. Now he wants to find the theorem of this statement. What is the theorem used in this statement?

Accepted Answer

Intermediate value theorem

Answer

Mean value theorem

Answer

Rolle’s theorem

Answer

None of these

Question 2

Which of the following graphs shows that according to the intermediate theorem $$f(x)$$ has a root in the interval $$[a,b]$$?

Accepted Answer

Answer

Answer

Both

Answer

None

Question 3

Find the value of $$'b'$$ such that $$f(x)={{x}^{3}}-3x+91$$ has a root in the interval $$(0,b)$$

Accepted Answer

$$(-13,7)$$

Answer

$$(-7,13)$$

Answer

$$(7,-13)$$

Answer

$$(-13,-7)$$

Question 4

A function $$f(x)=a{{x}^{3}}-30{{x}^{2}}+28x-47$$ has a root in the interval $$(0,1)$$. Then the value of a can be equal to

Accepted Answer

50

Answer

48

Answer

49

Answer

47

Question 5

The function $$f(x)=5{{x}^{103}}+2{{x}^{97}}-3{{x}^{91}}-93{{x}^{5}}$$

Accepted Answer

Has a root in the interval $$\left( 1,10 \right)$$

Answer

Has a root in the interval $$\left( -10,-1 \right)$$

Answer

Both of these

Answer

None of these