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

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Answer 1 · 2017-09-24T12:42:58

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

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

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]

What is the minimum value of g(x) = x^2+ 12x + 11?g(x)=x2+12x+11?g(x) = x^2+ 12x + 11? on the interval [-5,0][−5,0][-5,0]?