5.1-5.6 Flashcard

Front

What is the product rule in calculus?

Back

The product rule is a formula used to find the derivative of the product of two functions. If u(x) and v(x) are two functions, then the derivative of their product is given by: (u*v)' = u'v + uv'.

Front

What does it mean for a function to be always positive?

Back

A function is always positive if its output is greater than zero for all values in its domain. For example, the function g^2(x) is always positive because squaring any real number results in a non-negative value.

Front

Who is Judge Judy?

Back

Judge Judy is a television personality and former judge known for her courtroom show, 'Judge Judy', where she adjudicates small claims cases.

Front

Who is Yukon Cornelius?

Back

Yukon Cornelius is a character from the animated television special 'Rudolph the Red-Nosed Reindeer', known for being an adventurer who helps Rudolph.

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero. This means that if f(x) = c (where c is a constant), then f'(x) = 0.

Front

What is the chain rule in calculus?

Back

The chain rule is a formula for computing the derivative of the composition of two or more functions. If y = f(g(x)), then the derivative is given by: dy/dx = f'(g(x)) * g'(x).

Front

What is a derivative?

Back

A derivative represents the rate of change of a function with respect to a variable. It is a measure of how a function's output value changes as its input value changes.

Front

What is the significance of the first derivative test?

Back

The first derivative test is used to determine the local maxima and minima of a function. It involves analyzing the sign of the derivative to find critical points.

Front

What is a critical point in calculus?

Back

A critical point occurs where the derivative of a function is either zero or undefined. These points are potential locations for local maxima, minima, or points of inflection.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). In contrast, a relation can have multiple outputs for a single input.