MAT 21A Lecture Notes - Lecture 8: Tangent, Farad, Adverb

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21A
• Professor: Rohit Thomas

Document Summary

Mat21a - lecture 8 - 3. 1: tangents and the derivative at a point & 3. 2: the derivative as a. Slope of the graph y=f(x) at any point (a,b) lim h 0 f(a+h) f(a) h. This is the same as the tangent line to y=f(x) at (a,b) This is called the derivative of f(x) at x=a. Tells us how fast y is changing with respect to x. Find a common denominator: lim h 0. 3(3+h) h lim h 0 y 3. Using point-slope formula, plug in slope and given coordinates to find tangent line: Example 2: say the population of a bacterial colony is. How fast is the population changing after 4 hours? t2 + 9 + 1 t. = t2 + 9 + 1 t at t=4 f. Derivative of f(4+h) f(4) lim h 0 lim h 0 h. Plug in h=0: lim h 0. 3. 2: the derivative as a function part 1 f(a+h) f(a) lim h 0.