I just need 2, 8, and 18

PROBLEMS In problems 1 and 2 , each quotation is a statement about a quantitity of something changing over time. Let f{t) represent the quantity at time t. For each quotation, tell what f represents and whether the first and second derivatives of f are positive or negative. 1 . (a) " Unemployment rose again, but the rate of increase is smaller than last month." (b) "Our prots declined again. but at a slower rate than last month." (c) "The population is still rising and at a faster rate than last year." 2. (a) "The chi ld's temperature is still rising, but slower than it was a few hours ago.\" (b) "The number of whales is decreasing. but at a slower rate than last year." (c) "The number of people with the flu is rising and at a faster rate than last month." 3. Sketch the graphs of functions which are dened and concave up everywhere and which have (a) no roots. (b) exactly 1 root. (c) exactly 2 roots. ((1) exactly 3 roots. 4. On which intervals is the function in Fig. 11 (a) concave up? (b) concave down? 5. On which intervals is the function in Fig. 12 (a) concave up? (b) concave down? In problems 6 10, a function and values of x so that f '{x) = 0 are given. Use the Second Derivative Test to determine whether each point (x, f(x)) is a local maximum. a local minimum or neither 6. f{x):2x315x2+6 , x=0,5. 7. g(x)=x33x29x+7.x:l,3. s. h(x)=x48x22, x=2,0,2. 9. f{x) :sin5(x), x::rtf2,:t.3rd2 18. The function f(x) = e ( x-c) 2/(2b3 ) is called the Gaussian distribution, and its graph is a bell-shaped curve (Fig. 17) that occurs commonly in statistics. -(x-c)2 Gaussian f(x) = 1 e 2b2 (i) Show that f has a maximum at x = c . ( The Distribution value c is called the mean of this distribution.) (ii) Show that f has inflection points where x = c+ b and x = c-b . (The value b is called c-b C the standard deviation of this distribution. ) ctb Fig. 17