Question
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Identify the absolute minimum of g(x)=−2x2 −x+1 over [−2,4].

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Step 1

Absolute minimum:

The absolute minimum of a function f on the interval [a, b] will occur either at the endpoints [a, b] or at a critical point of f in [a, b]. That is, f’(c) = 0 for some c where a < c < b.

Step 2

Obtain the critical point of the function g(x) in [–2, 4]:

The given function is g(x) = –2x2x +1.

The given interval is [–2, 4].

The critical point of the function g(x) in [–2, 4] is obtained as (–1/4) from the calculation given below:

Step 3

Obtain the absolute minimum of the function g(x) in [–2, 4]:

Now substitute the values –2, –1/4, 4 for x in the function g(x) = –2x2 – x +1.

The absolute minimum of th...

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### Calculus 