What is the extreme Y(s)=(α^1)/s+(α^2)/(2s+6) ?

The extreme Y(s)=(α^1)/s+(α^2)/(2s+6) is Maximum(-6,-1/2)

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extreme Y(s)=(α^1)/s+(α^2)/(2s+6)

extreme points

Y (s) = \frac{α ^{1}}{s} + \frac{α ^{2}}{2 s + 6}

Maximum (- 6, - \frac{1}{2})

Solution steps

Find the critical points:

(- 6, - \frac{1}{2})

\frac{\partial ^{2} f}{\partial s ^{2}} = \frac{1}{s + 3}

D (s, α) = \frac{- s ^{6} + 6 s ^{5} α - 18 s ^{5} + 72 s ^{4} α - 135 s ^{4} + 324 s ^{3} α - 540 s ^{3} + 648 s ^{2} α - 1215 s ^{2} + 486 s α - 1458 s - 729}{s ^{4} ( s + 3 ) ^{6}}

Check the sign of at each critical point

Check critical point

(- 6, - \frac{1}{2}) :

Maximum

Maximum (- 6, - \frac{1}{2})

f (x) = 0.93

f (x) = f (x) = x + 3 x^{\frac{2}{3}}, - 10 \leq x \leq 1

f (x) = - x^{2} + 4

f (x) = 2.4

f (x) = 2 - x

What is the extreme Y(s)=(α^1)/s+(α^2)/(2s+6) ?
The extreme Y(s)=(α^1)/s+(α^2)/(2s+6) is Maximum(-6,-1/2)