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f '(x)<0 ? ∙ f(x)=0 ? f '(x)>0 ? ∙ ∙ ∙ x=0 ? f(x)=0 & x<0 ? f '(x)<0 ? ∙ ∙ ∙ x=0 ? ∙ f '(x)=0 ? ∙ f(x)=0 & x>0 ? ∙ f '(x)>0 ? y=0 & x<0 ? y'>0 ? ∙ ∙ ∙ x=0 ? y'=0 ? ∙ ∙ y'<0 ? ∙ y=0 & x>0 ? f '(x-)<0 & f '(x)=0 & f '(x+)>0 ? ∙ ∙ f '(x-)>0 & f '(x)=0 & f '(x+)<0 ? x=0 ? ∙ ∙ f(x)=0 ? ∙ y=0 & x<0 ? dy/dx=0 min ? ∙ x=0 ? ∙ y=0 & x>0 ? ∙ dy/dx=0 & x<0 ? y=0 x<0 ? ∙ y=0 dy/dx<0 ? ∙ ∙ ∙ x=0 ? ∙ dy/dx=0 x>0 ? ∙ y=0 dy/dx>0 ? f '<0 ⇨ f '=0 ⇨ f '>0 & x<0 ? f=0, x<0 ? ∙ f=0, x=0 ? ∙ f '>0 ⇨ f '=0 ⇨ f '<0 ? ∙ f=0, f '<0 ? ∙ f '<0 ⇨ f '=0 ⇨ f '>0 & x>0 ? ∙ ∙ ∙ f=0 & x>0 ? Use f'(x) notation to label the indicated points as shown ∙ ∙ f'(x)=0 ∙ ∙ ∙ ∙ ∙ ∙ f '(d) f '(b) f '(c) f '(a) f(a) f(c) a State each as '=0' '<0' or '>0' b c d e g h f '(g) f '(e) f '(h) f(e) f(h) f '(a) f '(b) f '(e) f '(c) f '(d) f(a) f(e) a b State each as '=0' '<0' or '>0' c d e g h i j f '(h) f '(0) f '(g) f '(i) f '(j) f(j) |