MATH 110 Lecture Notes - Lecture 40: Asymptote, Demand Curve, Inflection
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Examples: d dx f(x) = ef(x) * f e (x) Compute the derivative of y = e 9x e 9x * ( 9 = 9 9x. 3 e 3x 2 * d (4 e2t +t2 * d (2t dx e2t +t2 * ( + 1) Compute the derivative of (t) g dx e 3x (4. 3 e 3x 2 * ( e 3x * d (4. 2 e 2x + x 2x d ( x) (e dx. 2x + x d dx y = x 2x. ) (e x(e (4 d dx (e e. 2 x2 xe f (1) e. = 1 * e x/9 + x x/9 e. /9) e x/9 x (1 x = 9 ( /9) Continued: lim x ex = 0 and lim x ex = y = 0 = horizontal asymptote, no v. a. = ex > 0 for all x f (x) is always increasing.
