1.2-1.3 Review (Increasing/Decreasing Functions, Concavity)

Front

What does it mean for a function to be increasing on an interval?

Back

A function f is increasing on an interval if for any two points a and b in that interval, if a < b, then f(a) < f(b).

Front

True or False: A function can be both increasing and decreasing on the same interval.

Back

FALSE

Front

What is a constant function with a constant rate of change?

Back

A constant function is one where the output value does not change regardless of the input value, resulting in a rate of change of zero.

Front

What does it mean for a function to be increasing at a decreasing rate?

Back

A function is increasing at a decreasing rate if the slope of the function is positive but getting smaller as x increases.

Front

What is a decreasing function?

Back

A function f is decreasing on an interval if for any two points a and b in that interval, if a < b, then f(a) > f(b).

Front

What does it mean for a function to be decreasing with a constant rate of change?

Back

A function is decreasing with a constant rate of change if the slope of the function is negative and remains the same across the interval.

Front

What is the definition of concavity in a function?

Back

Concavity refers to the direction in which a function curves: a function is concave up if it opens upwards and concave down if it opens downwards.

Front

How can you determine if a function is concave up?

Back

A function is concave up if its second derivative is positive over an interval.

Front

How can you determine if a function is concave down?

Back

A function is concave down if its second derivative is negative over an interval.

Front

What is the relationship between the first derivative and increasing/decreasing functions?

Back

If the first derivative of a function is positive, the function is increasing; if it is negative, the function is decreasing.