Derivatives Practice

Front

What is the derivative of the function f(x) = x^4?

Back

The derivative is f'(x) = 4x^3.

Front

Where on a graph would you find a horizontal tangent line?

Back

A horizontal tangent line occurs where the derivative is zero. For example, at x = 0.

Front

Find the derivative of y = 4x^2 - 5x + 3.

Back

The derivative is y' = 8x - 5.

Front

What is the derivative of the function f(x) = 3x^3 + 2x^2 - x?

Back

The derivative is f'(x) = 9x^2 + 4x - 1.

Front

How do you find the derivative of a function using the power rule?

Back

The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1).

Front

What is the derivative of the function f(x) = sin(x)?

Back

The derivative is f'(x) = cos(x).

Front

What is the derivative of the function f(x) = e^x?

Back

The derivative is f'(x) = e^x.

Front

Find the derivative of y = ln(x).

Back

The derivative is y' = 1/x.

Front

What is the derivative of the function f(x) = x^2 + 3x + 2?

Back

The derivative is f'(x) = 2x + 3.

Front

What does it mean if the derivative of a function is zero at a point?

Back

It means that the function has a horizontal tangent line at that point, indicating a potential local maximum or minimum.