138 STEP 4. Review the Knowledge You Need to Score High
- The graph offis shown in Figure 7.7-4
and fis twice differentiable. Which of the
following has the largest value:
(A) f(−1)
(B) f′(−1)
(C) f′′(−1)
(D) f(−1) andf′(−1)–1 0fyxFigure 7.7-4
Sketch the graphs of the following functions
indicating any relative and absolute
extrema, points of inflection, intervals on
which the function is increasing, decreasing,
concave upward or concave downward.- f(x)=x^4 −x^2
- f(x)=
x+ 4
x− 4
Part B Calculators are allowed. - Given the graph off′in Figure 7.7-5,
determine at which of the four values ofx
(x 1 ,x 2 ,x 3 ,x 4 )f has:
(a) the largest value,
(b) the smallest value,
(c) a point of inflection,
(d) and at which of the four values ofx
doesf′′have the largest value.f ′x 1 x 4
xy(^0) x 2 x 3
Figure 7.7-5
- Given the graph offin Figure 7.7-6,
determine at which values ofxis
Figure 7.7-6(a) f′(x)= 0
(b) f′′(x)= 0
(c) f′a decreasing function.- A functionf is 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 whichfis
increasing or decreasing.
(b) Find wheref has its absolute extrema.
(c) Find wheref has points of inflection.
(d) Find the intervals wherefis concave
upward or downward.
(e) Sketch a possible graph off.