Question

1 point) Sketch the graph of the function y = x(4-2) - 103 In x. Indicate the transition points (local extrema and points of inflection) (Use symbolic notation and fractions where needed. Give your answer in the form of comma separated list of e-coordinates. Enter NULL in answer field if there is no such point.) Local maximum at = help (fractions) Local minimum at I= Inflection at I=

Answer 1

0 103 lon ( x > y = 40 dy 4-on dr -> 103 > 2 - dy - 2 + 103 2 거 dn² minimum Values Occur at boint Local manimum satisfying dy da (03 4-22- n 103 -> 4- 2x+ 40=20² 103 22 -4Xt103 - 0 > 202 4+ (16) 2-86103) 4 So, no real value of a exists. =) No local manunun or local minimum enist. tos dy 103 da? 2 2² > 2 1 - 103 2 V [Because of so

sou Local manimon at x = NULL Local Minimum at = NULL Inflexion at 103 2

Y -100 0 10 20 X -- 100 --200 --300

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Q2 y = V812 trio-x gnt ſlog ofnalo dy dr gx I AVя t 1 avion (-1) g ars 2/1o-x for dy 18 Vioon = 2ra 키 g (g) = 810 - 812-a. 810 N = 82 d²y dr² + Lo for x=810-403 82 41 - 9 4 (2) / 4/510-83 is point of maxima. So, 810 82

9 As d²4 dr 1 11 لیا۔ t 니 3. Jac (Vn} (V1o-n) for HER no inflession So, there is Local manimum at 405 41 at Local minimum = NULL NULL at x- point Inflession

Y 30 20 10 0 2 3 4 5 6 7 8 9 10 Х -10

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23. y = 4-an + the 11 6 V dy da -unt 40 6 dy 4* (-1 + 3) da -) x=0, na to Then dy - 4+20² da² –4 +210)² = -440 so, dy dn² at n-oc Na tvo! d²y da² -4 + 12 = 8 zo and a=t6 is Masina point of So, n=o'is pont of minima,

Manimum Local néninen So, Local at no lo a= [-roi ve T-VE, VE Joe = [15 And for inflexion sovint f'(x) = 0 >> 42222 0122 - nat 2 at +12 X- So, Inflenion

Y 40 30 20 -10 (0,4) -5 -4 0 4 5 X (-2.449, -2) (2.449, -2)