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Identify the absolute minimum of f(x)=2x2 +x+1 over [−2,3].

Question

Identify the absolute minimum of f(x)=2x2 +x+1 over [−2,3].

check_circleAnswer
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.

 

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Step 3
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Math

Calculus

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