What is the minimum value of #g(x) = x^2+ 12x + 11?# on the interval #[-5,0]#?

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Answer 1 · 2017-09-24T12:42:58

Minimum value of # g(x) = -24 # on the interval #[-5,0]#

#g(x) = x^2+12x+11 :. g^'(x) = 2x+ 12 :. g^('')(x) =2#.

Turning point :#g^'(x)=0 or 2x =12=0 or x= -6 #

Since # g^('')(x) =2 ; >0 #. Turning point is the minimum point.

But #x=-6# is beyond the interval # [-5,0]#. Since it is parabola

opening upwards, in the interval # [-5,0] ; g(-5) # will be of

minimum value , #:. g(5) = (-5)^2+12*(-5)+11 = -24 #

i.e # (-5,-24)#

graph{x^2+12x+11 [-80, 80, -40, 40]} [Ans]