Functions, Derivatives, Graphs Review

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

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

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

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

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).

Front

What is a local maximum?

Back

A local maximum is a point in the domain of a function where the function value is greater than or equal to the function values at nearby points.

Front

What is a local minimum?

Back

A local minimum is a point in the domain of a function where the function value is less than or equal to the function values at nearby points.

Front

What is concavity?

Back

Concavity refers to the direction of the curvature of a graph. A function is concave up if its graph is shaped like a cup (opening upwards) and concave down if it is shaped like a cap (opening downwards).

Front

What is a point of inflection?

Back

A point of inflection is a point on the graph of a function where the concavity changes.

Front

What does the second derivative test indicate?

Back

The second derivative test helps determine the concavity of a function and can indicate local maxima or minima based on the sign of the second derivative.

Front

What does it mean if g''(x) > 0?

Back

If g''(x) > 0, the function g(x) is concave up at that point.

Front

What does it mean if g''(x) < 0?

Back

If g''(x) < 0, the function g(x) is concave down at that point.