What is the instantaneous rate of change of #f(x)=1/(x^2-x+3 )# at #x=0 #?
2 Answers
Jan 20, 2018
1/9
Explanation:
find
(power rule:
plug in 0 for x:
Jan 20, 2018
Explanation:
#"the instantaneous rate of change of f(x) at x=0"#
#"is f'(0)"#
#"differentiate using the "color(blue)"chain rule"#
#"given "f(x)=g(h(x))" then"#
#f'(x)=g'(h(x))xxh'(x)larrcolor(blue)"chain rule"#
#f(x)=1/(x^2-x+3)=(x^2-x+3)^-1#
#rArrf'(x)=-(x^2-x+3)^-2xxd/dx(x^2-x+3)#
#color(white)(rArrf'(x))=-(2x-1)/(x^2-x+3)^2#
#rArrf'(0)=-(-1)/3^2=1/9#