Question

Consider the following graph of f(x) on the closed interval (0,5): 5 4 3 2 1 0 -1 0 1 2 3 5 6 (If the picture doesn't load, click here 95graph2) Use the graph of f(x) to answer the following: (a) On what interval(s) is f(x) increasing? (b) On what interval(s) is f(x) decreasing? (c) On what interval(s) is f(x) concave up? (d) On what interval(s) is f(x) concave down? (e) Where are the inflection points (both x and y coordinates) of f(x)?

Answer 1

Soln 2 on (3,4.4) on (3,4.4) on (0,3)U(4.4,5) According to the giun graph in a) as we know that, t(1) = 0 t (3)=0, ť (4.4) = 0 Since, ť(2) 20 on :: tm) is increasing b.) Since, ť(2) <0 on (0, 3) U (44,5) :: +(w) is decreasing since, t (1) = 0 , t (2)=0 t (3.5) = 0. From the giun graph. t" (w) >0 ou (0,1)U(2,3.5) *fcu) is concam upward on (0,1)U(2, 3-5) d) t (hiko on (1, 2) u (3-5,5) otu) is concam downward ou (1,2)U(3.5, 5) e) the inflection point of tim) is where t (n) = 0, the inflection point (1,5), (2,4) and (3.5, 4.5)

It g'(5)=0 and g(5)>0 thun has local minimum at n=95 gow Hence, n=s, is local minimum. Hence, 2nd option is correct. 3 a) (False). It tom) is conseel continuous on a closed interval, then find the absolute minimum and manunum you need to just consider ť (n) =0. is the fo (False) statenent. Since & In order to find absolute manina or initia we ham to on [a, b], We ham to consider t(a), f(b) and re-value where t(k)=0. الينابع EX с a b b. Absolute minima at nab, ť (b)=o. Absolute manima at n=c, ť (c) 70

b) (False). ť(()=0 thun cis a local militare or a manimum. the statenunt is false. Sif ť (c)=0 and t"(c)>o has local minima at n=c It t(C) = 0 and t (c) <0 has local marina at nae St t'(C)=0 and t" (c) =0 has inflichton point usc. () t (c) =0 Huu ce is an inflection point statement is Over (True) the ginn statement is
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