10.

(a) is increasing on

(b) is not decreasing anywhere.

(C) is concave up on and

(d) is concave down

(e) the -coordinates of all inflection points and

15-32. Find (a) the intervals on which is increasing, (b) open intervals on which is decreasing (c) the open intervals on which is concave up (d) the open intervals on which in concave down, and (e) live -coordinates of all inflection points.

15

Sign analysis for

(a) is increasing on since on

(b) is decreasing on since on

Note: one can take any value from the interval as a test value.

(c) Since on

is concave up on

(d) is nowhere concave down

(e) Since concavity does not change at any , therefore has no inflection point.

16.

Put

Sign analysis of

(a) on is increasing on

(b) on is decreasing on

(c) since on , therefore is nowhere concave up.

(d) Since on , therefore is Concave down on

(e) has no inflection point since does not change the concavity on

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differentiating twice w.r. t

Sign analysis of

(a)

(b)

Now put

Sign analysis of

(c) Since for is concave up on

(d) Since for is concave down on

(e) Since concavity chnages at , therefore is the coordinate of point of inflection.