Is #f(x)=(-3x^2-3x-2)/(x^2+x)# increasing or decreasing at #x=1#?
1 Answer
Jun 23, 2017
Explanation:
#"to determine if f(x) is increasing/decreasing at x = a"#
#• " if " f'(a)>0" then f(x) increasing at x = a"#
#• " if " f'(a)<0" then f(x) decreasing at x = a"#
#"differentiate f(x) 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))^2#
#g(x)=-3x^2-3x-2rArrg'(x)=-6x-3#
#h(x)=x^2+xrArrh'(x)=2x+1#
#f'(x)=((x^2+x)(-6x-3)-(-3x^2-3x-2)(2x+1))/(x^2+x)^2#
#rarrf'(1)=(2.(-9)-(-8).3)/4#
#color(white)(rArrf'(1))=6/4=3/2#
#"since " f'(1)>0" then f(x) is increasing at x = 1"#
