Deetermine, without graphing, ehether the given quaratic function has a maximum value or a minimum value and then find the valur. f(x) = 2x^2-12x

Question
Quadratics
asked 2021-03-09
Deetermine, without graphing, ehether the given quaratic function has a maximum value or a minimum value and then find the valur. f(x) = 2x^2-12x

Answers (1)

2021-03-10
Obtain the critical points as follows. f'(x)=0 d/(dx)(2x^2-12x)=0 4x-12=0 x=12/4 x=3 Thus, the critical point is x=3 f''(x)=4>0 at x=3 Therefore, minimum exist at x=3 Substitute x=3 in f(x)=2x^2-12x and obtain that, f(3)=2(3)^2-12(3) =2(9)-36 =18-36 =-18 Thus, the quadratics function has a minimum value, the value is −18. image
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