Is #f(x)=(12x^2-16x-12)/(x+2)# increasing or decreasing at #x=5#?

1 Answer
Jim G.
Sep 25, 2017

#"increasing at "x=5#

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"#

Related questions
See all questions in Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)
Impact of this question
1304 views around the world
You can reuse this answer
Creative Commons License