Question

Asked Apr 5, 2019

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

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*) = –2*x*^{2} – *x *+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*) = –2*x*2 – *x *+1.

The absolute minimum of th...

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