MATH1151 Chapter Notes - Chapter 3: Implicit Function, Mean Value Theorem, Quotient Rule
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In this chapter we will look at: the definition of the derivative, the differentiation rules (high school stuff, the mean value theorem (obvious, but important, applications like. Implicit differentiation e l"h pital"s rule: lim x!0 x sin x 2 tan x sin x. The straight line that it looks like will have a well-de ned slope and that is what we shall de ne to be the slope of the graph at x0. That is, the difference between the f (x) and the tangent line is small compared to the distance h to x0. Remember that this means that for any there exists > 0 such that. |f (x0 + h) ((mx0 + b) + mh)| h whenever |h| < . Suppose that f : (a, b) r and that x0 (a, b). We shall say that f has slope or derivative s at x0 if f (x0 + h) f (x0) lim h!0 h exists and equals s.
