AP Calculus AB: Unit 5 Quest

Front

What does it mean for a function f'(x) to be positive and increasing?

Back

It means that the slope of the tangent line to the graph of f is positive and that the rate of change of f'(x) is increasing, indicating that f is becoming steeper.

Front

What is a relative minimum in the context of a function's graph?

Back

A relative minimum is a point where the function value is lower than the values of the function at nearby points.

Front

What is a point of inflection?

Back

A point of inflection is where the graph of a function changes its concavity, meaning it changes from concave up to concave down or vice versa.

Front

What does it mean for a function to be concave up?

Back

A function is concave up on an interval if its second derivative is positive on that interval, indicating that the graph is curving upwards.

Front

What is the First Derivative Test?

Back

The First Derivative Test is a method used to determine relative extrema of a function by analyzing the sign of the first derivative before and after critical points.

Front

What is the Extreme Value Theorem (EVT)?

Back

The EVT states that if a function is continuous on a closed interval, then it must have both an absolute maximum and an absolute minimum on that interval.

Front

How do you identify critical points of a function?

Back

Critical points occur where the first derivative is zero or undefined.

Front

What is the significance of the second derivative?

Back

The second derivative provides information about the concavity of the function and can indicate points of inflection.

Front

What does it mean for a function to be concave down?

Back

A function is concave down on an interval if its second derivative is negative on that interval, indicating that the graph is curving downwards.

Front

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

Back

If f'(x) > 0, the function f is increasing; if f'(x) < 0, the function f is decreasing.