ROC, Tangent Lines, and Derivative

Front

What is the derivative of a function?

Back

The instantaneous rate of change of the function.

Front

What does f '(x) = 0 indicate about the tangent line?

Back

The tangent line is horizontal.

Front

What does the derivative represent in terms of a graph?

Back

The slope of the tangent line at a given point.

Front

If a function has a negative derivative, what does that imply?

Back

The function is decreasing.

Front

What is the limit definition of the first derivative?

Back

The derivative is defined as the limit of the average rate of change as the interval approaches zero.

Front

What does a positive derivative indicate about a function?

Back

The function is increasing.

Front

What is the relationship between the derivative and the slope of the tangent line?

Back

The derivative at a point gives the slope of the tangent line at that point.

Front

What does it mean if the second derivative is positive?

Back

The function is concave up.

Front

What does it mean if the second derivative is negative?

Back

The function is concave down.

Front

What is the geometric interpretation of a derivative?

Back

It represents the slope of the tangent line to the curve at a specific point.