Question

5. (4pts, each) In each part, list the point (A-E) on the graph off whose x-coordinate satisfies the given conditions. (a) f'(x) > 0. and F"(x) > 0 (b) f'(x) <0. and f"(x) = 0 (c) f'(x) = 0.and f"(x) < 0 6. (12pts) Find all critical numbers of f(x) = x + Then use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum. Show your work to get a full credit!

Answer 1

Page No. Date : ONOS Solutions! a) f'io and fuso Print E i's طع ܢܨܐܬܟܫܢܐ i's 20 To the left of E the function is cncreasing in f'w so and to the right of few also increasinglesf'ca) 20 and "=0 point B to the left of or the function is decreasing le famoco and to the night of a the fu constant ily 4"600 ý ful and "00<0 point A At A the function allaven's Deake_value, ie, poco and to the right of A. aday decreases it free) <0. Extra question Isaution fm at u f'm) 1+ 41-12) fire) to function ONO a I-4 22 - At enitical point, f'(u) =D 1-Y = 0 = 1/2 => x² = 4. => x = +2 *M = wote h 0-412) At a = 2 for cake) tous, even have local minimuon at 122) At l 2-2 f"60 - Lo (Thus, we have locel maximum a 12-2 2 lo