Unit 3 AP Calculus AB review

Front

What is the definition of speed in the context of calculus?

Back

Speed is the absolute value of the velocity of an object, which is the derivative of its position function with respect to time.

Front

How do you find the acceleration of a particle given its position function s(t)?

Back

Acceleration is found by taking the second derivative of the position function s(t) with respect to time t.

Front

What does it mean for a particle's acceleration to be zero?

Back

When a particle's acceleration is zero, it means that the particle is moving at a constant speed; it is not speeding up or slowing down.

Front

How do you determine when two functions have parallel tangent lines?

Back

Two functions have parallel tangent lines when their derivatives (slopes) are equal at a certain point.

Front

What is the derivative of the function f(x) = 4e^{2x}?

Back

The derivative is f'(x) = 8e^{2x}.

Front

What is the derivative of the function g(x) = 3x^3?

Back

The derivative is g'(x) = 9x^2.

Front

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

Back

The slope of the tangent line at a point is found by evaluating the derivative of the function at that point.

Front

What is the product rule in differentiation?

Back

The product rule states that if u(x) and v(x) are functions, then the derivative of their product is u'v + uv'.

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y = f(g(x)), then the derivative is dy/dx = f'(g(x)) * g'(x).

Front

What is the natural logarithm function and its derivative?

Back

The natural logarithm function is ln(x), and its derivative is 1/x.