Graphs of Functions and Derivatives 111
[−π,π] by [−2,2]
Figure 7.2-7
Using the [[ Zero] function of the calculator, you obtainx= 1 .25331 is a zero of f′on
0,
π
2
]
. Sincef′(x)=cos(x^2 ) is an even function,x=− 1 .25331 is also a zero on
[
−
π
2
,0
]
.
(See Figure 7.2-8.)
p –1.2533 1.2533
2
p
2
f′ –
f
+ –
[]
decr. incr. decr.
x
Figure 7.2-8
Thus,fis increasing on [− 1 .2533, 1.2533].
TIP • Bubble in the right grid. You have to be careful in filling in the bubbles especially when
you skip a question.
First Derivative Test and Second Derivative Test for Relative Extrema
First Derivative Test for Relative Extrema
Letf be a continuous function andcbe a critical number off. (Figure 7.2-9.)
Figure 7.2-9