Calculus AB (review 1)

Front

If a function has a derivative that is negative, what does that tell you?

Back

The function is decreasing.

Front

Find the derivative of the function f(x) = x^4 cos(x).

Back

f'(x) = x^4 cos(x) + 4x^3 sin(x).

Front

What is the limit of the function as x approaches a certain value?

Back

1/4.

Front

The acceleration function is the first derivative of which function?

Back

velocity.

Front

What is the limit of the function as x approaches a certain value?

Back

12.

Front

Define the derivative of a function.

Back

The derivative represents the rate of change of a function with respect to its variable.

Front

What does it mean if the second derivative of a function is positive?

Back

The function is concave up.

Front

What is the Fundamental Theorem of Calculus?

Back

It links the concept of differentiation and integration, stating that differentiation and integration are inverse processes.

Front

What is the definition of a limit?

Back

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

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).