Question

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

Answer 1

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

Explanation:

`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]