Graphs of Functions and Derivatives 135Answer: fhas a relative minimum atx=−2. (See Figure 7.6-6.)
f′
x
f–20decr. 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.
yxf′′–3 0 34Figure 7.6-8Answer: f′is concave upward on (−∞, 0). (See Figure 7.6-9.)f ′′ incr. decr.+–
concave
upwardconcave
downwardx
f ′′′
f ′0Figure 7.6-9