Download presentation
Presentation is loading. Please wait.
1
Curve Sketching: Sketching 𝑓 from 𝑓′
Honors Calculus Keeper 22
2
Review: Sketch 𝑓′(𝑥) 𝒇(𝒙) 𝒇′(𝒙)
3
Review: Sketch 𝑓′(𝑥) 𝒇(𝒙) 𝒇′(𝒙)
4
Review: Sketch 𝑓′(𝑥) 𝒇(𝒙) 𝒇′(𝒙)
5
Review: Sketch 𝑓′(𝑥) 𝒇(𝒙) 𝒇′(𝒙)
6
Review: Sketch 𝑓′(𝑥) 𝒇(𝒙) 𝒇′(𝒙)
7
Review: Sketch 𝑓′(𝑥)
8
From 𝑓′ sketch 𝑓 and 𝑓′′
9
From 𝑓′ sketch 𝑓 and 𝑓′′
10
From 𝑓′ sketch 𝑓 and 𝑓′′
11
From 𝑓′ sketch 𝑓 and 𝑓′′
12
From 𝑓′ sketch 𝑓 and 𝑓′′
13
From 𝑓′ sketch 𝑓 and 𝑓′′
14
Draw a possible Graph of 𝑓(𝑥) given the information below.
𝑓(𝑥) is continuous 𝑓 3 =2 𝑓 ′ 𝑥 >0, −∞, 0 , 3, ∞ 𝑓 ′ 𝑥 <0, 0,3 𝑓 ′ 𝑥 =0 at 𝑥=0, 𝑥=3
15
Draw a possible Graph of 𝑓(𝑥) given the information below.
𝑓(𝑥) is continuous 𝑓 ′ 𝑥 <0 (−∞,1) 𝑓 ′ 𝑥 >0 (1,∞) 𝑓 ′ 𝑥 is undefined at 𝑥=1 𝑓 ′′ 𝑥 <0 at −∞,1 𝑈(1,∞)
16
Draw a possible Graph of 𝑓(𝑥) given the information below.
𝑓(𝑥) is continuous 𝑓 ′ 𝑥 <0, −∞, 2 , 2, ∞ 𝑓′(𝑥) is undefined at 𝑥=2 𝑓 ′′ 𝑥 <0, when 𝑥<2 𝑓 ′′ 𝑥 >0 at 𝑥=0, 𝑥>2
17
Draw a possible Graph of 𝑓(𝑥) given the information below.
𝑓(𝑥) has a jump at 𝑥=−2 𝑓 ′ 𝑥 >0; −∞, −2 , −2, ∞ 𝑓 ′′ 𝑥 <0; −∞, −2 𝑓 ′′ 𝑥 >0; −2, ∞
Similar presentations
![Area Between Two Curves 7.1. Area Formula If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the.](/19/5716150/big_thumb.jpg "Area Between Two Curves 7.1. Area Formula If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the.>")
