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

sagnuhh 2021-03-09 Answered

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

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Expert Answer

Leonard Stokes
Answered 2021-03-10 Author has 7144 answers

Obtain the critical points as follows. \(f'(x)=0 \frac{d}{dx}(2x^2-12x)=0\ 4x-12=0 x=\frac{12}{4} x=3\) 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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