\n| Monotonia de $f$<\/td>\n | \u00a0$ \\searrow $<\/td>\n | $1$<\/td>\n | \u00a0$ \\nearrow $<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Confirma-se que $f’$ muda de sinal quando passa da esquerda para a direita de zero, concluindo-se que $f$ passa de decrescente para crescente.<\/p>\n No entanto, repare-se que:<\/p>\n \\[\\begin{array}{*{20}{c}}
\n{ \\bullet \\begin{array}{*{20}{l}}
\n{\\mathop {\\lim }\\limits_{x \\to {0^ – }} f\\left( x \\right) = \\mathop {\\lim }\\limits_{x \\to {0^ – }} \\left( {{x^2} + 1} \\right) = 1}&{}&{ \\bullet f\\left( 0 \\right) = 1}&{}&{ \\bullet \\mathop {\\lim }\\limits_{x \\to {0^ + }} f\\left( x \\right) = \\mathop {\\lim }\\limits_{x \\to {0^ + }} x = 0}
\n\\end{array}} \\\\
\n{{\\text{A fun\u00e7\u00e3o n\u00e3o \u00e9 cont\u00ednua no ponto de abcissa 0}}{\\text{, pois }}\\mathop {\\lim }\\limits_{x \\to {0^ + }} f\\left( x \\right) \\ne f\\left( 0 \\right).{\\text{ }}}
\n\\end{array}\\]<\/p>\n Assim, dos c\u00e1lculos acima, conclui-se:<\/p>\n \n- ${f\\left( 0 \\right) = 1}$ N\u00c3O \u00c9 M\u00cdNIMO relativo, pois $f\\left( 0 \\right) > \\mathop {\\lim }\\limits_{x \\to {0^ + }} f\\left( x \\right)$;<\/li>\n
- ${f\\left( 0 \\right) = 1}$ N\u00c3O \u00c9 M\u00c1XIMO relativo, pois $f$ \u00e9 estritamente decrescente em $\\left] { – \\infty ,0} \\right]$.<\/li>\n<\/ul>\n
Portanto, a fun\u00e7\u00e3o $f$ n\u00e3o admite extremo relativo no ponto de abcissa $0$.<\/p>\n A an\u00e1lise do gr\u00e1fico da fun\u00e7\u00e3o permite esclarecer as conclus\u00f5es escritas acima:<\/p>\n<\/p>\n |