Verse 48: The function (% MathType! MTEF! 2! 1! + -% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2% da9iaadIhadaahaaWcbeqaaiaaiodaaaGccqGHsislcaaIZaGaamiE% amaaCaaaleqabaGaaGOmaaaakiabgkHiTiaaiMdacaWG4bGaey4kaS% IaaGymaaaa! 41CD! Y = {x ^ 3} – 3{x^2} – 9x + 1) covariates on which of the following intervals?

Defined set: D= R . Derivative: \ (% MathType! MTEF! 2! 1! + -% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa% Gaeyypa0JaaG4maiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsisl% caaI2aGaamiEaiabgkHiTiaaiMdaaaa! 3F0B! Y ‘= 3 {x ^ 2} – 6x – 9\)

Consider .\ (% MathType! MTEF! 2! 1! + -% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa% Gaeyypa0JaaGimaiabgkDiElaaiodacaWG4bWaaWbaaSqabeaacaaI% YaaaaOGaeyOeI0IaaGOnaiaadIhacqGHsislcaaI5aGaeyypa0JaaG% imaiabgsDiBpaadeaaeaqabeaacaWG4bGaeyypa0JaaG4maiabgkDi% ElaadMhacqGH9aqpcqGHsislcaaIYaGaaGOnaaqaaiaadIhacqGH9a% qpcqGHsislcaaIXaGaeyO0H4TaamyEaiabg2da9iaaiAdaaaGaay5w% aaaaaa! 5996! Y ‘= 0 \Rightarrow 3{x^2} – 6x – 9 = 0 \Leftrightarrow \left[\begin{array}{l}x=3\Rightarrowy=-26\\x=-1\Rightarrowy=6\end{array}\right\)

Variation table:

Covariate function on intervals \ (% MathType! MTEF! 2! 1! + -% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq% GHsislcqGHEisPcaaMc8Uaai4oaiaaykW7cqGHsislcaaIXaaacaGL% OaGaayzkaaaaaa! 3F58! \ Left ({- \ infty \,; \, – 1} \right)\) and \ (% MathType! MTEF! 2! 1! + -% feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca% aIZaGaaGPaVlaacUdacaaMc8Uaey4kaSIaeyOhIukacaGLOaGaayzk% aaaaaa! 3E62! \ Left ({3 \,; \, + \ infty } \right)\)

Therefore, the function is covariate on the interval (4, 5)