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 _____________.

Short answer

The solution is,

has critical point

greater than zero

not applicable

decreasing

concave down

decreasing

Step-by-step solution

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 localid="1650310283718" $f\text{'}$ is not applicable.

If localid="1650310291250" $f\text{'}$ is negative, then localid="1650310298040" $f$is decreasing.

If localid="1650310301356" $f\text{'}\text{'}$ is negative, then localid="1650310306026" $f$is concave down.

If localid="1650310309909" $f\text{'}\text{'}$ is negative, then localid="1650310313535" $f\text{'}$ is decreasing.