MATH 1300 Quiz: MATH1300 Quiz 7 2015 Fall

• School: CU-Boulder
• Department: Mathematics
• Course: MATH 1300
• Professor: All

Document Summary

= 0: find the rst and second derivatives of f with respect to x. f(cid:48)(x) = x2(1/x) (ln x)(2x) x3( 2/x) (1 2 ln x)(3x2) x4 f(cid:48)(cid:48)(x) = x6. [you may use either a number line or interval notation. ] Looking at the sign of the rst derivative, we see that f is increasing on (0, e1/2) and decreasing on (e1/2, ). Looking at the sign of the second derivative, we see that f is concave up on (e5/6, ) and concave down on (0, e5/6): list any local extrema of f and the values of x at which they occur. The function f has a local max of 1 and decreasing afterwards. 2e at x = e1/2 because f is increasing until x = e1/2: list any in ection points for the graph of f . The only in ection point is (e5/6, concave down to concave up.