1.1-bo'lim : Ko'rib chiqish: Funktsiyalar
6. The farq koeffitsienti \(f\left( x \right)\) funksiyasi quyidagicha aniqlanadi:
\[\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}\]\(g\left( x \right) = 6 - {x^2}\) uchun farq koeffitsientini hisoblang.
Maslahat: Funktsiya endi \(g\left( x \right)\) deb nomlanganligidan hayajonlanmang, farq koeffitsienti hozirda \(f\) o'rniga \(g\) bilan bir xil ishlaydi. Shunday qilib, \(g\left( {x + h} \right)\) ni hisoblang, so'ngra suratni hisoblang va nihoyat farq koeffitsientini hisoblang.
Yechim
\[g\left( {x + h} \right) = 6 - {\left( {x + h} \right)^2} = 6 - {x^2} - 2xh - {h^2}\]
2-qadam
\[g\left( {x + h} \right) - g\left( x \right) = 6 - {x^2} - 2xh - {h^2} - \left( {6 - {x^2}} \right) = - 2xh - {h^2}\]
3-qadam
\[\frac{{g\left( {x + h} \right) - g\left( x \right)}}{h} = \frac{{ - 2xh - {h^2}}}{h} = - 2x - h\]