Q. 1 - Calculus

Question

Fill in the blanks if a relationship exists. If there is nothing of substance to say, write “not applicable.”

 If $f\text{'}$  has a zero, then $f$ ___________ .

 If $f$ is increasing, then $f\text{'}$  is ____________.

 If $f$ is positive, then $f\text{'}$  is ______________.

 If $f\text{'}$  is negative, then $f$ is ______________.

 If $f\text{'}\text{'}$ is negative, then $f$ is _________________.

 If $f\text{'}\text{'}$  is negative, then $f\text{'}$ is _____________.

Step-by-Step Solution

Answer

The solution is,

has critical point

greater than zero

not applicable

decreasing

concave down 

decreasing

Step 1. Given Information

We have to fill in the correct relationship.

Step 2. Fill in the blanks.

 If $f\text{'}$ has a zero, then $f$ has critical point.

 If $f$ is increasing, then $f\text{'}$  is greater than zero.

 If $f$ is positive, then $f\text{'}$  is not applicable.

 If $f\text{'}$  is negative, then $f$ is decreasing.

 If $f\text{'}\text{'}$  is negative, then $f$ is concave down.

 If $f\text{'}\text{'}$  is negative, then $f\text{'}$  is decreasing.