Question

Sa se stabileasca maximul sau minimul urmatoarelor functii:
f(x)=x²-5
f(x)=-12x²+31x-1
f(x)=-x²-2x+1
f(x)=0,5x²+0,7x-0,31
As vrea sa stiu cum se stabileste minimul sau maximul pls

Answer 1

f(x)=x²-5
a=1>0 => f admite mimim
$y \: min = - \frac{delta}{4a}$
Δ=b²-4ac  
 Δ=0²-4·1·(-5)
 Δ=20
$y \: min = - \frac{20}{4 \times 1} = - 5$
f(x)=-12x²+31x-1
a=-12<0 => f admite maxim
$y \: max = - \frac{delta}{4a}$
 Δ=b²-4ac
 Δ=31²-4·(-12)·(-1)
 Δ=961-48
 Δ=913
$y \: max = - \frac{913}{4 \times ( - 12)} = \frac{913}{48}$