Graphs of Functions and Derivatives 139- Given the graph off′in Figure 7.7-7, find
where the functionf
(a)has its relative extrema.
(b)is increasing or decreasing.
(c)has its point(s) of inflection.
(d) is concave upward or downward.
(e)if f(0)=1 andf(6)=5, draw a sketch
of f.Figure 7.7-7- Iff(x)=|x^2 − 6 x− 7 |, which of the
following statements aboutf are true?
I. f has a relative maximum atx=3.
II. f is differentiable atx=7.
III. f has a point of inflection atx=−1.- How many points of inflection does the
graph ofy=cos(x^2 ) have on the interval
[−π,π]?
Sketch the graphs of the following functions
indicating any relative extrema, points of
inflection, asymptotes, and intervals where
the function is increasing, decreasing,
concave upward or concave downward.- f(x)= 3 e−x^2 /^2
- f(x)=cosxsin^2 x[0, 2π]
- Find the Cartesian equation of the curve
defined byx=
t
2
,y=t^2 − 4 t+1. - Find the polar equation of the line with
Cartesian equationy= 3 x−5. - Identify the type of graph defined by the
equationr= 2 −sinθand determine its
symmetry, if any. - Find the value ofkso that the vectors
〈3,− 2 〉and〈1,k〉are orthogonal. - Determine whether the vectors〈5,− 3 〉and
〈5, 3〉are orthogonal. If not, find the angle
between the vectors.
7.8 Cumulative Review Problems
(Calculator) indicates that calculators are
permitted.
- Find
dy
dx
if (x^2 +y^2 )^2 = 10 xy. - Evaluate limx→ 0
√
x+ 9 − 3
x.
- Find
d^2 y
dx^2
ify=cos(2x)+ 3 x^2 −1. - (Calculator) Determine the value ofksuch
that the function
f(x)={
x^2 −1, x≤ 1
2 x+k, x> 1is continuousfor all real numbers.