Qhov haujlwm twg yog monotonic?

2024 Tus sau: Elizabeth Oswald | [email protected]. Kawg hloov kho: 2024-01-13 00:07

A monotonic muaj nuj nqi yog ib txoj haujlwm uas yog txhua yam tsis nce lossis tsis txo qis. Ib qho kev ua haujlwm yog monotonic yog tias nws thawj derivative (uas yuav tsum tsis tu ncua) tsis hloov kos npe.

Koj paub li cas yog tias muaj nuj nqi yog monotonic?

Test rau cov haujlwm monotonic hais: Piv txwv tias muaj nuj nqi txuas ntxiv ntawm [a, b] thiab nws txawv ntawm (a, b). Yog hais tias tus derivative loj dua xoom rau tag nrho x hauv (a, b), ces qhov kev ua haujlwm nce rau [a, b]. Yog hais tias tus derivative tsawg dua xoom rau tag nrho x hauv (a, b), ces qhov kev ua haujlwm yuav txo qis rau [a, b].

Puas yog cov haujlwm nruj me ntsis monotonic?

Tsis tas li, ib qho haujlwm tuaj yeem hais tias yog nruj me ntsis monotonic ntawm ntau qhov txiaj ntsig, thiab yog li muaj qhov hloov pauv ntawm qhov ntau ntawm tus nqi. Piv txwv li, yog tias y=g (x) yog nruj me ntsis monotonic ntawm qhov ntau [a, b], ces nws muaj qhov hloov pauv x=h(y) ntawm qhov ntau [g(a), g(b)], tab sis peb tsis tuaj yeem hais tias tag nrho cov haujlwm muaj qhov hloov pauv.

Is E XA monotonic muaj nuj nqi?

Tus derivative ntawm exp(x) yog exp(x) thiab exp(x) yog ib txwm zoo, yog li, exp(x) yog ib qho kev ua haujlwm nce ntxiv.

piv txwv monotonic yog dab tsi?

Monotonicity of a Function

Functions hu ua monotonic yog tias lawv nce lossis txo qis hauv lawv cov npe tag nrho. Piv txwv: f(x)=2x + 3, f(x)=log(x) , f(x)=e^x yog cov piv txwv ntawm nce kev ua haujlwm thiab f(x)=-x⁵ thiab f(x)=e^{-x yog cov piv txwv ntawm kev txo qis.}