MATH 10A Lecture 11: Math 10A - 1-27 Lecture - Equations of the Tangent Line
Document Summary
Key idea: the derivative of f at a represents: The instantaneous rate of change of f at a. The slope of the tangent line to the graph of f at x=0. Definition: a function f is differentiable at x=a if after zooming in on the graph enough x=a, the graph starts to look like a line. That is, f"(0) is undefined. f is positive on (-1, ) f is negative on (- , -1) f" is positive on (- , 1) u (4, ) f" is negative on (1,4) pretend there"s a graph here shut up. F" is positive -> f is increasing. F" is negative -> f is decreasing. Example: find an equation for the tangent line to f(x)=x3 at x=10. = 300 (f (10+h) f (10))/(h) lim h 0 (10+h 3 1000)/(h) lim h 0 (1000+300 h+30h2+h3 1000)/(h) (300h+30h2+h3)/(h) (300+30h+h2) lim h 0 lim h 0 lim h 0.
