Analytical Apps of the Derivative

A function is increasing when its derivative is ___________________.

• positive

• negative

• increasing

• decreasing

A function has a point of inflection when its derivative ___________________.

• equals zero

• equals zero or does not exist

• changes sign

• changes from increasing to decreasing or vice versa

A function is concave down when its derivative is ___________________.

• positive

• negative

• increasing

• decreasing

When the derivative of a function is negative, the function is _______________.

• increasing

• decreasing

• concave up

• concave down

When the second derivative of a function is positive, the function is _______________.

• increasing

• decreasing

• concave up

• concave down

A function has a critical number when its derivative ___________________.

• equals zero

• equals zero or does not exist

• changes sign

• changes from increasing to decreasing or vice versa

A function has a point of inflection when its second derivative ___________________.

• equals zero

• equals zero or does not exist

• changes sign

• changes from increasing to decreasing or vice versa

When the derivative of a function is increasing, the function is _______________.

• increasing

• decreasing

• concave up

• concave down

When the derivative of a function changes from positive to negative, the function has a __________________.

• relative maximum

• relative minimum

• point of inflection

• possible point of inflection.

A function has a possible point of inflection when its second derivative _________________.

• changes from increasing to decreasing or vice versa

• equals zero or does not exist

• has a relative minimum

• has a relative maximum