AP Calculus AB
Vocabulary (from Mrs. Nichol's Classroom Blog)
- Derivative – A function which gives the slope of a curve; that is, the slope of the line tangent to a function. The derivative of a function f at a point x is commonly written f ‘(x).
- Slope of a curve – A number which is used to indicate the steepness of a curve at a particular point. The slope of a curve at a point is defined to be the slope of the tangent line. Thus the slope of a curve at a point is found using the derivative.
- Tangent line – A line that touches a curve at a point without crossing over. Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line.
- Difference quotient – For a function f, the formula . This formula computes the slope of the secant line through two points on the graph of f. These are the points with x-coordinates x and x + h. The difference quotient is used in the definition the derivative.
- Differentiable – A curve that is smooth and contains no discontinuities or cusps. Formally, a curve is differentiable at all values of the domain variable(s) for which the derivative exists.
- Instantaneous Rate of Change – The rate of change at a particular moment. Same as the value of the derivative at a particular point. For a function, the instantaneous rate of change at a point is the same as the slope of the tangent line. That is, it’s the slope of a curve. Note: Over short intervals of time, the average rate of change is approximately equal to the instantaneous rate of change.
- Implicit Differentiation – A method of finding the derivative of a function or relation in which the dependent variable is not isolated on one side of theequation. For example, the equation x² + xy – y² = 1 represents an implicit relation.
- Logarithmic Differentiation – A method for finding the derivative of functions such as y = xsin x and , where the derivative is cumbersome or impossible with direct differentiation techniques.
3.2 Derivative as a Function - Day 1
3.2 Derivative as a Function - Day 2
Throwback Thursday - Exponential Functions and Logarithms
3.3 Product and Quotient Rules
3.4 Rates of change
3.5 Higher derivatives
3.6 Trigonometric functions
3.7 The chain rule
3.8 Derivatives of inverse functions
3.9 Derivatives of general expo and log functions
3.10 Implicit differentiation
3.11 Related rates
Chapter 4: Applications of The Derivative
Chapter 5: The Integral
Chapter 6: Applications of The Integral