MATH 121 Lecture 8: 3.5

• School: University of Alabama
• Department: MATH
• Course: MATH 121
• Professor: Wein

Document Summary

Section 3. 5- derivatives: numerical and graphical viewpoints: derivative: the derivative of the function f at x is defined as: f x lim)(" The notation (cid:4666)(cid:1876)(cid:4667) with respect to x. is read f prime of x . If x is a value in the domain of f and if. Difference quotient derivative of f(x) derivative of f(x) at x=a af exits, then f is differentiable at x. haf hxf xf. Slope of the secant line slope of the tangent line=rise/run slope of tangent line at x=a. Average rate of change instantaneous rate of change instantaneous rate of change at x=a. Average velocity instantaneous velocity instantaneous velocity at x=a: approximations of derivative: Sometimes, we also use the alternative fomula: with a small value of h. with a small value of h. Example 1: estimate the derivative from the table of average rates of change.