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CALC Derivative Concepts 1
Contributed by: Heseltine
f '(x)<0
?
∙
f(x)=0
?
f '(x)>0
?
∙
∙
∙
x=0
?
f(x)=0 & x<0
?
f '(x)<0
?
∙
∙
∙
x=0
?
∙
f '(x)=0
?
∙
f(x)=0 & x>0
?
∙
f '(x)>0
?
y=0 & x<0
?
y'>0
?
∙
∙
∙
x=0
?
y'=0
?
∙
∙
y'<0
?
∙
y=0 & x>0
?
f '(x-)<0 & f '(x)=0 & f '(x+)>0
?
∙
∙
f '(x-)>0 & f '(x)=0 & f '(x+)<0
?
x=0
?
∙
∙
f(x)=0
?
∙
y=0 & x<0
?
dy/dx=0
    min
?
∙
x=0
?
∙
y=0 & x>0
?
∙
dy/dx=0 & x<0
?
y=0
x<0
?
∙
y=0
dy/dx<0
?
∙
∙
∙
x=0
?
∙
dy/dx=0 x>0
?
∙
y=0
dy/dx>0
?
f '<0 ⇨ f '=0 ⇨ f '>0 & x<0
?
f=0, x<0
?
∙
f=0, x=0
?
∙
f '>0 ⇨ f '=0 ⇨ f '<0
?
∙
f=0, f '<0
?
∙
f '<0 ⇨ f '=0 ⇨ f '>0 & x>0
?
∙
∙
∙
f=0 & x>0
?
Use f'(x) notation to
label the indicated
points as shown
∙
∙
f'(x)=0
∙
∙
∙
∙
∙
∙
f '(d)
f '(b)
f '(c)
f '(a)
f(a)
f(c)
a
State each as '=0' '<0' or '>0'
b
c
d
e
g
h
f '(g)
f '(e)
f '(h)
f(e)
f(h)
f '(a)
f '(b)
f '(e)
f '(c)
f '(d)
f(a)
f(e)
a
b
State each as '=0' '<0' or '>0'
c
d
e
g
h
i
j
f '(h)
f '(0)
f '(g)
f '(i)
f '(j)
f(j)
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