Question

Identify the absolute minimum of f(x)=2x^{2} +x+1 over [−2,3].

Step 1

The given function is *f(x) =2x^2+x+1* over the [-2,3].

Step 2

Obtain the local minimum of the function as follows.

Use the second derivative test to determine the local minima of the function.

__Second derivative test:__

- If f"(a) <0 and f′ (a) =0, then there is a local maximum at
*x=a*. - If f"(a) >0 and f′ (a) =0, then there is a local minimum at
*x=a*.

Consider the function *f(x) =2x^2+x+1.*

Differentiate the function *f(x) =2x^2+x+**0 *and equate to zero.

Step 3

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