MATH 110 Study Guide - Midterm Guide: Quotient Rule, Asymptote, Maxima And Minima
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Find where the given function f (x) is decreasing. f (x) = 2 , ) (c) ( 1, 0) ( 2. 3 , ) (d) ( , 0) (3, ) (e) (0, 3. We need to nd where f(cid:48)(x) < 0. Find the critical points and determine the sign of f(cid:48)(x). f(cid:48)(x) = 2x3 x2 3x. You can determine the sign of f(cid:48)(x) by testing points in each interval. Furthermore, you can use the sign of each factor as in the following table: since f(cid:48)(x) is negative on the intervals ( , 1) and (0, 3. 2 ), the x interval ( , 1) ( 1, 0) (0, 3. 2 , ) ( 3 function f (x) is decreasing on ( , 1) (0, 3. 2 ). (2x 3) (x + 1) f(cid:48)(x: find all the relative extrema of the function f (x) = 3 ln(x) 6x2, domain of f(x):(0, ) Take the derivative and nd the critical points.
