Is #f(x)=(12x^2-16x-12)/(x+2)# increasing or decreasing at #x=5#?
1 Answer
Sep 25, 2017
Explanation:
#"to determine if f(x) is increasing at x = a evaluate"#
#f'(x)" at x = a"#
#• " if "f'(a)>0" then f(x) is increasing at x = a"#
#• " if "f'(a)<0" then f(x) is decreasing at x = a"#
#"differentiate using the "color(blue)"quotient rule"#
#"given "f(x)=(g(x))/(h(x))" then"#
#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#
#g(x)=12x^2-16x-12rArrg'(x)=24x-16#
#h(x)=x+2rArrh'(x)=1#
#rArrf'(x)=((x+2)(24x-16)-(12x^2-16x-12))/(x+2)^2#
#rArrf'(5)=(728-208)/49>0#
#rArrf(x)" is increasing at x = 5"#
