Dabo Calculus AB Exam 2024 S1 part 2

Front

What is continuity in calculus?

Back

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. It must be defined, and the left-hand and right-hand limits must exist and be equal.

Front

What does it mean for a function to be differentiable?

Back

A function is differentiable at a point if it has a defined derivative at that point, meaning the function has a tangent line at that point and is continuous there.

Front

How do you find points of inflection?

Back

Points of inflection occur where the second derivative of a function changes sign, indicating a change in the concavity of the graph.

Front

What is the limit definition of a derivative?

Back

Front

What is the equation of a tangent line?

Back

Front

How do you evaluate limits involving trigonometric functions?

Back

Front

What is the relationship between the first and second derivatives?

Back

The first derivative indicates the slope of the function (increasing or decreasing), while the second derivative indicates the concavity (concave up or down) and helps find points of inflection.

Front

What is a normal line in calculus?

Back

The normal line to a curve at a given point is perpendicular to the tangent line at that point. Its slope is the negative reciprocal of the slope of the tangent line.

Front

How do you find the slope of a tangent line at a point?

Back

To find the slope of the tangent line at a point x=a, calculate the derivative f'(a).

Front

What is the significance of critical points?

Back

Critical points occur where the first derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.