Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f left parenthesis x right parenthesisequalsx squared minus 6 x minus 9; left bracket 0 comma 7 right bracket

The absolute minimum value of the function over the interval [0,7] is -18.

Step-by-step explanation:

The given function is

Differentiate f(x) with respect to x.

Equate f'(x)=0  to find the critical points.

The critical point is x=3.

Differentiate f'(x) with respect to x.

Since f''(x)>0 for all values of x, therefore the critical point is the point of minima and the function has no absolute maximum value.

3 ∈ [0,7]

Substitute x=3 in the given function to find the absolute minimum value.

Therefore the absolute minimum value of the function over the interval [0,7] is -18.

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