3.3: Derivatives and Shapes of Graphs
Def 2. A. function of is increasing
on un
interval I if for
all
४
2
in I where x, <x2,
We have f(x) <f(x₂]
on
an
interval I it for
2. A. function f is decreasing
Example:
'all
M
X, Xz 21
in I where x, xx₂, we have fox,) sh)
2
a) on what
What can
open interval is ncreasing?
we say about f' on these intervals?
(Incresing: (a, b) V(sd) f'(x) 20 on these intercals
b) on what open interval is I decreasing
What can we say about f' on these interals?
decreasing: (b,c) f'(xsco on this interval
Increasing/Decreasing Test
1. If fers to old ca
2. If exsed on are
Example
an
८
that interval
interval, then feks is increasing on
interval, then fees in decreasing on that interial
t
Find the intervals whore facs = 2x3 3x²-36x is always increasing
or decreasing.
2
2
⋅f ( x ) = 6 x² + bx-36 = ((x²+x-6)
2
=6(x+3)(x-2).
f4x7=0> x=-32
6643/18-2/F16
X2-3
1
-34842+
-
+ inc
[dec.
tina
By
B-IUT, f' is 20 or 20 on each of
(-80-3)U (-3,2) √√(2,00)
fl fi fi
Def 2. A. function of is increasing
on un
interval I if for
all
४
2
in I where x, <x2,
We have f(x) <f(x₂]
on
an
interval I it for
2. A. function f is decreasing
Example:
'all
M
X, Xz 21
in I where x, xx₂, we have fox,) sh)
2
a) on what
What can
open interval is ncreasing?
we say about f' on these intervals?
(Incresing: (a, b) V(sd) f'(x) 20 on these intercals
b) on what open interval is I decreasing
What can we say about f' on these interals?
decreasing: (b,c) f'(xsco on this interval
Increasing/Decreasing Test
1. If fers to old ca
2. If exsed on are
Example
an
८
that interval
interval, then feks is increasing on
interval, then fees in decreasing on that interial
t
Find the intervals whore facs = 2x3 3x²-36x is always increasing
or decreasing.
2
2
⋅f ( x ) = 6 x² + bx-36 = ((x²+x-6)
2
=6(x+3)(x-2).
f4x7=0> x=-32
6643/18-2/F16
X2-3
1
-34842+
-
+ inc
[dec.
tina
By
B-IUT, f' is 20 or 20 on each of
(-80-3)U (-3,2) √√(2,00)
fl fi fi
