Increasing and decreasing intervals Quiz 1

Question 1

Which of the following statements is/are correct if $$f(x)$$ is an increasing function?

Accepted Answer

The below graph represents an increasing function as the value of $$x$$ increases. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/0f29799e-4d5f-4f45-b899-c0fd5c22ee5e3018475149252450532.png"/>

Answer

$$	ext{{f}'(x) < 0}$$

Answer

The below graph represents an increasing function as the value of $$x$$ increases. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/dd6be88c-5b54-406f-bbdd-dab271f8d230557215074476892217.png"/>

Answer

$$	ext{{f}'(x)=0}$$

Question 2

Which of the following graphs will represent the graph of decreasing function in the interval $$\left( 1,\infty  \right)$$

Accepted Answer

Answer

Answer

Both $$(a)$$ and $$(b)$$

Answer

None of the above

Question 3

From the given graph, which of the following statements are correct? $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/b011f576-7b95-4853-826e-a9e6b34fd90c2918536290003025700.png"/>

Accepted Answer

The graph has a local minimum in the third quadrant and a local minimum in the 1st quadrant.

Answer

The graph has a local maximum in the third quadrant and a local minimum in the 1st quadrant.

Answer

The graph has a local minimum in the first quadrant and a local maximum in the 1st quadrant.

Answer

The graph has a local minimum in the third quadrant and a local maximum in the 1st quadrant.

Question 4

For the function $$f(x)={{x}^{3}}-\dfrac{{{x}^{2}}}{2}-2x+1$$, find the interval where the function increases?

Accepted Answer

$$\left( \dfrac{	ext{2}}{	ext{3}}	ext{,1} ight)$$

Answer

$$	ext{(-2,-1)}$$

Answer

$$	ext{(1,2)}$$

Answer

None of the above

Question 5

For the function $$f(x)={{x}^{3}}-79{{x}^{2}}+271x-37$$, which of the following statements are correct?

Accepted Answer

The graph will increase at $$\left( -\infty ,1.77 \right)\cup \left( 50.9,\infty  \right)$$ and decrease at $$\left( 1.77,50.9 \right)$$.

Answer

The graph will decrease at $$\left( -\infty ,1.77 \right)$$ and increase at $$\left( 1.77,50.9 \right)$$.

Answer

The graph will increase at $$\left( 50.9,\infty  \right)$$ and decrease at $$\left( 1.77,50.9 \right)$$.

Answer

The graph will decrease at $$\left( -\infty ,1.77 \right)\cup \left( 50.9,\infty  \right)$$ and increase at $$\left( 1.77,50.9 \right)$$.