Sec 2.7: Derivative and Rates of Change Def: The difference quotient of ƒ at x0 with increment h. The derivative of a function ƒ at a point x0 Def: Example: Example: Find the derivative of ƒ at Find the difference quotient of ƒ at x0 = 2 with increment h. Example: Find the derivative of ƒ at Equivalent Expression The derivative of a function ƒ at a point x0 Example: Find

Sec 2.7: Derivative and Rates of Change Def: The difference quotient of ƒ at x0 with increment h. The derivative of a function ƒ at a point x0 Def: The slope of the secant to the curve f(x) at the point x0 is Def: The slope of the tangent to the curve f(x) at the point x0 is Def: Def: average velocity Def: instantaneous velocity Term-111

Sec 3.1: Tangents and the Derivative at a Point Term-111

Sec 2.7: Derivative and Rates of Change Def: The difference quotient of ƒ at x0 with increment h. The derivative of a function ƒ at a point x0 Def: The slope of the secant to the curve f(x) at the point x0 is Def: The slope of the tangent to the curve f(x) at the point x0 is Def: Def: average velocity Def: instantaneous velocity Def: average rate of change Def: instantaneous rate of change

Sec 2.7: Derivative and Rates of Change Suppose y is a quantity that depends on another quantity x. Thus y is a function of x and we write y = f(x). Temperature in Dhahran T depends on time t If x changes from x1 to x2 , then the change in x (also called the increment of x) Give an example for quantity that depends on another and the corresponding change in is The instantaneous rate of change of ƒ with respect to x at The average rate of change of ƒ with respect to x over the interval Term 102 Term 102 Term 121