Where do the absolute extrema of #f(x) = -3x^2+7x# on the interval #[1, 3]# occur?

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Answer 1 · 2017-10-13T13:07:10

Absolute maximum is at #(1.16, 4.083) # and
and absolute minimum at interval #[1,3]# is # (3,-6)#

#f(x)= -3x^2+7x [1,3] :. f^'(x)= -6x +7#

Critical point: #f^'(x=)=0 :. -6x+7= 0 or x = 7/6# ,

which lies in interval #[1,3] ; f^'(1) = (+) and f^'(2) =( -)#

# :. x=7/6~~1.16 # is the absolute maximum ;

#:. f(7/6) ~~4.083# , So absolute maximum is at

#(1.16, 4.083) and f(1)= 4 , f(3)= -6 # and absolute minimum

in interval #[1,3]# is # (3,-6)# [Ans]