Graphs of Functions and Derivatives 135
Answer: fhas a relative minimum atx=−2. (See Figure 7.6-6.)
f′
x
f
–2
0
decr. incr.
–+
Figure 7.6-6
- (See Figure 7.6-7.) Givenfis twice differentiable, arrange f(10),f′(10),f′′(10)
from smallest to largest.
(^010)
y
x
f
Figure 7.6-7
Answer: f(10)=0,f′(10)>0 since fis increasing, andf′′(10)<0 since fis
concave downward. Thus, the order isf′′(10),f(10),f′(10).
- (See Figure 7.6-8.) Find the values ofxwhere f′is concave up.
y
x
f′′
–3 0 3
4
Figure 7.6-8
Answer: f′is concave upward on (−∞, 0). (See Figure 7.6-9.)
f ′′ incr. decr.
+–
concave
upward
concave
downward
x
f ′′′
f ′
0
Figure 7.6-9