Review December 2nd

Front

What is the derivative of x^4 cos(x)?

Back

The derivative is x^4 cos(x) + 4x^3 sin(x).

Front

How do you find dy/dx for the equation x^3 + y^3 = 36?

Back

dy/dx = -x^2/y^2.

Front

What determines speed in terms of velocity?

Back

Speed is determined by |v(t)|.

Front

How can you determine if a particle is switching directions?

Back

Find where velocity switches signs.

Front

When is a particle's speed decreasing?

Back

A particle's speed is decreasing if its velocity and acceleration have different signs.

Front

What is the definition of a derivative?

Back

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

Front

What does the notation f'(x) represent?

Back

f'(x) represents the derivative of the function f at the point x.

Front

What is the relationship between velocity and acceleration?

Back

Velocity is the derivative of position, while acceleration is the derivative of velocity.

Front

What does it mean if acceleration is positive?

Back

If acceleration is positive, the velocity of the particle is increasing.

Front

What does it mean if acceleration is negative?

Back

If acceleration is negative, the velocity of the particle is decreasing.