导数的综合应用 专题训练

导数的综合应用专题训练

fxaxbxcxd abcdabcd

abcdabcd

a

b

fc

abcd

a

b

fc

abcd

fx

xxmx

fx

mb ba a

fx

f

m fxx

fx

f

m fx

xfxf

x

xxa

a

xxaaxx

fxxxfxxfxfa

x

axxx

a

x

x

a

t

tattt

fx

x x xx

gttttt

gtttttgtgt

gtg

a

x

aa

x

ax mx mn x

xxxxPmn

Dyaxa

D

a

f

xxmx

mn

xx

xxmmnf

mn

mnmn

D

a

ayfxx时，有fxf x

Fxxfxf x

Fxxfx

x x x

f

x

f

xx

x

x

x

xf

x

f

x

xf

x

Fx

Ux

Fx

Uxxfx

Fxxfx

x

xfxFx

x

Uxxfx

UfUxxfx

xFx

x

xfxx

UfUxxfx

xxxFxxfxFxFx

fxxgxxa

x

xx

fxgx

a

xx

fxgx

fxgx

gxxax

x

gxa

fx

x

fxxxxx

fx

x

fxxxxx xx

x

x

x

x

x

x

x

x

kxx

fxf

gxa

a a

a

a

x

k

kxx

kxx

x

k

x

kxx

x

kxx

k

xx

fx

xx

fx

x

x

x

xx

xx

f

xx

f

x

a

a

f

x

a

fx

x

fx

f

x

a

x

fx

xx

f

x

x

xf

x

fx

xf

x

fx

kfxf

k

fx

xaxa

fxx

fx

xx xxf

xx

fx

xaxxxx

a

f

xfx x aa x aa

xax

xax

x

xaxxxxf

xxf

xxxx

x

xxx

xx

xxxx

xxxx

x

xaxx

xx

x

xxxx

t x t t

t

tt t

t t

t

t

t

xxfxx

x

Rx

xxx

Cxx

fx

Mfx

Mfxfxfx

Px

MPx

MPx PxRxCxxx

x

x

xMPxPxPxxx

x

xPxxx

xx

x

Px

x

x

Px

x

Px

x

Px

MPxxx

x

x

MPxMPx

fx

xf

x

ffffff

ffffff

x

f

x

fx

x

f

x

fx

x

fx

f，所以

ffff

fff

fxx

xax

a

f

x

a

gx

gxx fxx

f

x

a

gx

gxx

x

xx x

xgx

x

gx

xgx

gxg

aa

fxaxbx

xab

xfxf

ab

ab

ab

ab

f

xaxb

f

abx

x

gx

x

gxg

x

ab

ba

aa

gxx

xgx

gxx

x

gx gaa

ab

a

ab

fxxaxbxc

xx

fxxx

x

fxafxb

f

xxaxb

xaxb

xxxxxxfxfxxxxfxfxxxf

xfxxx

fxafxb

fxx

fxxfxx

fxxfxx

a fxaxaxgxxx

xii

fxigx

a

axxfxf

g

axxfxf

g

x

a

gx a

fx

x

a

x

a

a

x

xii

fxigxff

x

g

x

x

g

x

a

yfx

xf

xfx

gxxfxx

gxxfxxgxxf

xfx

gxgyfx

gx

gxg

gx

fxxmxxmmfx

m

f f

m

mmm

m

m

m

m

ggxxx

xgxxxx

gx

fx

x

x

a

f

xaxa

gx

gxgxgxx

x

mgx

m gxgxgx

x

g

ggx

gx

x

gx

g

mgx

m

fxxa

x

a

fxx

fxxa

xx x

a

f

xfx

a

xaf

x

xa

f

x

fxaf

xax

xa

xx

x

xx

x

gxxa

x xx

xx

hxxax

xhxx

x

xx

hxxax

xhxx

ax

a

hx

a

a

x

ax

x

hxxax

xxax

xaxxxa

gx

xax

x xx

a

x

hx

a

gxgxg

gxgxg a

a

x

x

xx x xx

gx

gx

a

a

gxg

a

fxxx

fx

x

fxax

a f

xxxx

f

x

x

x

x

f

x

x

f

x

x

f

x

fx

fxxxx

gxa

ga

a

a

gxa

ga

a

a

gx

hxx

x

hx

hxxxx

hx

h

hx

fxxhxxax

a

gxxx

gxxx

gx

g

xx

x

fxxxxxaxxaxxa

x a

xxxax

fxax

a

x

xfxxxaxa

fxaxaxx

x

fx

afx

x

fx fx

gxaxa

x

fxxgxfx

gx

ggx

gxx

x

gxgx

x

gx