What are the critical values, if any, of #f(x) = -3x^2+x-1#?

1 Answer
Dec 22, 2016

Answer:

The critical value is a maximum at #(1/6,-11/12)#

Explanation:

We must differentiate and do a sign chart

We use

#(x^n)'=nx^(n-1)#

#f(x)=-3x^2+x-1#

#f'(x)=-6x+1#

#f'(x)=0#, when #-6x+1=0#, #=>#, #x=1/6#

#f(1/6)=-3/36+1/6-1=-11/12#

We can do our sign chart

#color(white)(aaaa)##x##color(white)(aaaaa)##-oo##color(white)(aaaaa)##1/6##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##f'(x)##color(white)(aaaaa)##+##color(white)(aaa)##0##color(white)(aaa)##-#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##uarr##color(white)(aa)##-11/12##color(white)(aaa)##darr#

The critical value is a maximum at #(1/6,-11/12)#