ISRO previous paper 2013, Computer Science question 49, set A

What is the least value of the function f(x) = 2x²-8x-3 in the interval [0,5] ?
(a) -15
(b) -7
(c) -11
(d) -3

Answer is (a),

f '(x) = 2x-8

Let  f '(x) = 4x-8=0,
then, x=2,
substitute x=2 to the f ", but here no need to substitue in f ".

f ''(x) = 4 >0 (positive >> Minimum occurs at this point),

Refer this:
above question similar to Example 3  in below link:

https://www.math.wvu.edu/~hjlai/Words2Algebra/MinMax_Closed_Interva.pdf