CPM Calc Ch. 5 Review

Front

What is a derivative?

Back

A derivative represents the rate of change of a function with respect to a variable. It is a fundamental concept in calculus.

Front

How do you find the derivative of a function?

Back

To find the derivative, apply differentiation rules such as the power rule, product rule, quotient rule, and chain rule.

Front

What does it mean if a function has a positive first derivative?

Back

A positive first derivative indicates that the function is increasing.

Front

What does it mean if a function has a negative second derivative?

Back

A negative second derivative indicates that the function is concave down, meaning it is curving downwards.

Front

What is the limit of a function?

Back

The limit of a function is the value that the function approaches as the input approaches a certain point.

Front

What is the quotient rule in differentiation?

Back

The quotient rule states that if you have a function that is the quotient of two functions, the derivative is given by (f/g)' = (f'g - fg')/g².

Front

What is the product rule in differentiation?

Back

The product rule states that if you have a function that is the product of two functions, the derivative is given by (fg)' = f'g + fg'.

Front

How do you find the equation of a tangent line?

Back

To find the equation of a tangent line, use the point-slope form: y - y₁ = m(x - x₁), where m is the derivative at the point (x₁, y₁).

Front

What is the significance of the tangent line?

Back

The tangent line represents the instantaneous rate of change of the function at a specific point.

Front

What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that the limit does not approach a finite value.