3.1 Calculus Review

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero. It represents the slope of the tangent line to the function at that point.

Front

What does it mean for a function to be increasing on an interval?

Back

A function f(x) is increasing on an interval if for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

How do you find the derivative of a function using the definition?

Back

To find the derivative using the definition, use the formula: f'(x) = lim (h -> 0) [(f(x+h) - f(x))/h].

Front

What is the Alternate Definition of Derivative?

Back

The Alternate Definition of Derivative states that the derivative of f at a point x is given by f'(x) = lim (h -> 0) [(f(x) - f(x-h))/h].

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

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

Back

The derivative of a function at a given point is equal to the slope of the tangent line to the graph of the function at that point.

Front

What is the significance of the point where the derivative is zero?

Back

A point where the derivative is zero may indicate a local maximum, local minimum, or a point of inflection on the graph of the function.

Front

Back

Front

What is the power rule in differentiation?

Back

Front

What is the quotient rule for differentiation?

Back