MATH 3770 Final: MATH 3770 Iowa 3770 Final Review Fa 2018
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1 f (x) lim h 0 kx k e e f(x) = ef(x) x = ex. Find the following derivatives : ( kx e ) ( x e ) (e x2 ( 5x e ( t +t+1 e: find the intervals when the function is increasing and the intervals where this function is. Also find the absolute extrema in the interval [-1,1]. In fact an exponential function is never 0, so we always factor any exponentials out and discard when solving equations. The critical points in [-1,1] are x=0. f(0)=1, f(1)= 2 x2 2 x2 = e x2: find the intervals of concavity and the. = e x2 inflection points of the function (x) (x) f . Note in the above step we factored the expression to separate the exponential part out. This is an important step in solving equations or inequality involving exponentials. e x2 > 0. So the graph is concave up in ( 1.
