This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 xcoordinate of each point at which f attains an absolute maximum value or an absolute
minimum value. For each xcoordinate you give, state whether f attains an absolute maximum or
an absolute minimum. 5
on
m
:2
Fa (b) Find the xcoordinate 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 xintercepts 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 xyplane 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 yintercepts — 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: ...
View
Full
Document
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.
 Fall '10
 waldron

Click to edit the document details