Ch4-3WS - lq‘il — RB 5'5 5. Let f be a function that is...

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Unformatted text preview: lq‘il — RB 5'5 5. Let f be a function that is even and continuous on the closed interval [~ 3, 3]. The function f and its derivatives have the properties indicated in the table below. I. u (a) Find the x-coordinate of each point at which f attains an absolute maximum value or an absolute minimum value. For each x-coordinate you give, state whether f attains an absolute maximum or an absolute minimum. 5 on m :2 Fa (b) Find the x-coordinate of each point 'of inflection on the graph of f. Justify your answer. (c) In the xy -plane provided below, sketch the graph of a function with all the given characteristics of f. l me — HE'S 5. Let f be the function defined by f(x) = sing—x — sin x fer 0‘ s x s (a) Find the x-intercepts of the graph of f. (b) Find the intervals on which f is increasing. (c) Find the absolute maximum value and the absolute minimum value of f. Justify your answer. 1990— A60 6. Let f be the function that is given by f(x) = ax + b xz—C and that has the following properties. (i) The graph of f is symmetric with respect 'to the y—axis. (ii) .lim f(x)= +00 x—-2+ (iii) f'(1) = —2 (a) Determine the values of a, b, and c. (b) Write an equation for each vertical and each horizontal asymptote of the graph of f. (c) Sketch the graph of f in the xy-plane provided below. Name: Date: Math 604 — Curve Sketch Exercise Sketch 1 x" Use the grid below to sketch a graph of the continuous function y = f (x) with the a 1 m S S O P e r e h W S w a n .1 1m 5 m < c x d < ,m 04 L = )r as cm .m_41_#0 : m.) __ __ m,» r3))_ x p_15(( g((fl\” nrJrJfrJrJ Numb. 0.10. e. rm f. f’(x)<0 for x<—3 and x>5 g. f”(x)<0 for x>1 h.. f”(x)>0 for x<1 Date: Name: Sketch 2 Analyze and sketch the graph of y = x3 + 3):2 # 24x -— 30 Step 1 ~ Find the first derivative Step 2 . Find the 2“d derivative Consider the following a) Domain and Range ‘0) x—intercepts and y-intercepts — find and plot them c) Vertical Asymptotes (1) Horizontal Asymptotes e) Critical values — find and plot them if) Possible inflection points — find and plot them g) Limit as it goes to + or — infinity h) Sign chart for the derivative to determine regions of increase and decrease i) Sign chart for the 2nd derivative to determine regions of concave up and concave down Draw a set of axes and sketch the graph. Name: j) Use the grid below to make a sketch using first and second derivatives for the fimction y = 6xe". Date: ...
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This note was uploaded on 02/16/2012 for the course CALCULUS 0064 taught by Professor Waldron during the Fall '10 term at Broward College.

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Ch4-3WS - lq‘il — RB 5'5 5. Let f be a function that is...

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