AP Calculus Review - Limits, Derivatives, and Integrals

Front

What does the second derivative of position represent?

Back

The acceleration of an object at any given time.

Front

What is the derivative of csc(x)?

Back

-csc(x)cot(x)

Front

What does the slope of a position-time graph indicate?

Back

The velocity of an object.

Front

How do you find the average rate of change?

Back

Average rate of change = (Change in height) / (Change in time). Example: From 3 to 5 years old, if height changes by 8 inches, the average rate of change is 4 inches per year.

Front

Where can a graph be continuous but not differentiable?

Back

At points where there are sharp corners or cusps, such as x = b and d.

Front

Define a limit in calculus.

Back

A limit is the value that a function approaches as the input approaches a certain point.

Front

What is the Fundamental Theorem of Calculus?

Back

It links the concept of differentiation and integration, stating that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x)dx = F(b) - F(a).

Front

What is the derivative of sin(x)?

Back

cos(x)

Front

What is the relationship between the first derivative and the graph of a function?

Back

The first derivative indicates the slope of the tangent line to the graph, showing where the function is increasing or decreasing.

Front

What does a negative second derivative indicate about a function's concavity?

Back

The function is concave down.