MA 3972-MA-Book April 11, 2018 17:21166 STEP 4. Review the Knowledge You Need to Score High
- Given the graph offin Figure 8.6-6,
determine at which values ofxis:
(a) f′(x)= 0
(b) f′′(x)= 0
(c) f′a decreasing functionyx– (^1543210)
f
Figure 8.6-6
- A functionfis continuous on the interval
[−2, 5] withf(−2)=10 andf(5)=6 and
the following properties:
INTERVALS (−2, 1)X=1 (1, 3) X= 3 (3, 5)
f′ + 0 − undefined +
f′′ − 0 − undefined +(a) Find the intervals on whichf is
increasing or decreasing.
(b) Find wherefhas its absolute extrema.
(c) Find wherefhas points of inflection.
(d) Find the intervals wherefis concave
upward or downward.
(e) Sketch a possible graph off.- Given the graph off′in Figure 8.6-7, 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) iff(0)=1 and f(6)=5, draw a sketch
off.6xf′y(^03)
Figure 8.6-7
- If f(x)=|x^2 − 6 x− 7 |, which of the
following statements about fare true?
I. fhas a relative maximum atx=3.
II. fis differentiable atx=7.
III. fhas 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]