Math 65A Chapter on Derivatives

These flashcards cover the fundamental concepts and definitions related to derivatives from Chapter 3 of Math 65A.

What is the basic idea behind the derivative of a function?

The derivative measures the rate of change of a function at a given point.

What symbol is commonly used to denote the derivative of a function?

The most common symbols for the derivative are f'(x), df/dx, or Df.

What is the difference quotient formula?

Difference Quotient (DQ) is defined as DQ = (f(x+h) - f(x))/h.

What is the limit definition of the derivative?

The limit definition is df/dx = lim (h -> 0) [(f(x+h) - f(x))/h].

When calculating the derivative, what should you do first?

First take the difference quotient and simplify it.

How do you evaluate the derivative as a function?

By calculating the limit of the difference quotient as h approaches 0.

Can the derivative of a function also be graphed?

Yes, the derivative represents the slope of the tangent line and can be graphed.

What can affect the slope of a tangent line on a curve?

The slope of the tangent line varies depending on the point on the curve.

What is the instantaneous rate of change?

The instantaneous rate of change at a point on a curve is equivalent to the value of the derivative at that point.

What is the primary purpose of using limits in derivatives?

Limits help define the behavior of functions as they approach specific points, allowing us to find the derivative.