Graphs of functions and their derivatives

Front

What is the derivative of a function?

Back

The derivative of a function is the instantaneous rate of change of the function with respect to its variable.

Front

What does a negative derivative indicate about a function?

Back

If a function has a negative derivative, it indicates that the function is decreasing.

Front

What does a positive derivative indicate about a function?

Back

If a function has a positive derivative, it indicates that the function is increasing.

Front

What is the relationship between a function and its derivative at a maximum point?

Back

At a maximum point, the derivative of the function is zero.

Front

What is the relationship between a function and its derivative at a minimum point?

Back

At a minimum point, the derivative of the function is zero.

Front

How can you determine the slope of a tangent line to a curve at a point?

Back

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

Front

What is the graphical representation of a derivative?

Back

The graph of the derivative of a function shows the slope of the tangent line to the original function at each point.

Front

What does the second derivative tell us about a function?

Back

The second derivative indicates the concavity of the function: if positive, the function is concave up; if negative, concave down.

Front

What is the significance of critical points in relation to derivatives?

Back

Critical points occur where the derivative is zero or undefined, indicating potential maximum or minimum values.

Front

How do you find the derivative of a polynomial function?

Back

To find the derivative of a polynomial function, apply the power rule: bring down the exponent and decrease the exponent by one.