Unit 2 Derivative Review

Front

Back

Front

What is the equation of the line tangent to f(x) = 4x^2 + 2x - 1 at x = 0?

Back

y = 2x - 1

Front

A particle's speed is decreasing if:

Back

its velocity and acceleration have different signs.

Front

Which of the following determines speed?

Back

|v(t)|

Front

What is the equation of the tangent to the curve f(x) = 4x^2 + 2x - 1 at the point x = 0?

Back

y = 2x - 1

Front

Define the derivative of a function.

Back

The derivative of a function measures the rate at which the function's value changes as its input changes.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = nx^{n-1}.

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to differentiate equations where y is not isolated on one side.

Front

What does the second derivative tell us about a function?

Back

The second derivative indicates the concavity of the function and can determine points of inflection.

Front

What is the relationship between velocity and acceleration?

Back

Velocity is the derivative of position with respect to time, while acceleration is the derivative of velocity with respect to time.